Processing math: 2%

CBSE Questions for Class 12 Commerce Maths Three Dimensional Geometry Quiz 2 - MCQExams.com

The projection of the join of the two points (1,4,5),(6,7,2) on the line whose d.s's are (4,5,6) is
  • 1777
  • 76
  • 21
  • 79
If the d.cs of two lines are connected by the equations l+m+n=0,l2+m2n2=0, then angle between the lines is
  • π3
  • π4
  • π6
  • π2
The direction cosines of a line which is equally inclined to axes, is given by
  • \pm \dfrac{1}{3}
  • \pm \dfrac{1}{\sqrt{3}}
  • 1
  • 0
The equation of the plane passing through (2, -3, 1) and is normal to the line joining the points (3, 4, -1) and (2, -1, 5) is given by
  • x+5y-6z+19=0
  • x-5y + 6z-19=0
  • x+5y+6z+19=0
  • x-5y-6z-19=0
The equation of the plane containing the line 
\vec r = \hat i + \hat j + t\left( {2\hat i + \hat j + 4\hat k} \right), is
  • \vec r.\left( {\hat i + 2\hat j - \hat k} \right) = 3
  • \vec r.\left( {\hat i + 2\hat j - \hat k} \right) = 6
  • \vec r.\left( { - \hat i - 2\hat j + \hat k} \right) = 3
  • None of these
A line passes through the points (6, -7, -1) and (2, -3, 1). The direction cosines of the line so directed that the angle made by it with the positive direction of x-axis is acute, is?
  • \dfrac{2}{3}, -\dfrac{2}{3}, -\dfrac{1}{3}
  • -\dfrac{2}{3}, \dfrac{2}{3}, \dfrac{1}{3}
  • \dfrac{2}{3}, -\dfrac{2}{3}, \dfrac{1}{3}
  • \dfrac{2}{3}, \dfrac{2}{3}, \dfrac{1}{3}
If P be the point (2,6,3) then the equation of the plane trough P, at right angles to OP, where  'O' is the origin is
  • 2x+6y+3z=7
  • 2x-6y+3z=7
  • 2x+6y-3z=49
  • 2x+6y+3z=49
The equation of the plane passing through (a,b,c) and parallel to the plane r.(\hat{i}+\hat{j}+\hat{k})=2 is,
  • x+y+z=1
  • ax+by+cz=1
  • x+y+z=a+b+c
  • None of these
Angle between the lines 3x=6y=2z and 3x+2y+z-5=0=x+y-2z-3 is?
  • \dfrac{\pi}{6}
  • \dfrac{\pi}{3}
  • \dfrac{\pi}{4}
  • \dfrac{\pi}{2}
The points i + j + k, \, i + 2j, \, 2i+2j+k,\, 2i+3j+2k are
  • collinear
  • coplanar but not collinear
  • non-coplanar
  • none
If the dr's the line are (1+\lambda, 1-\lambda, 2) and it makes an angle {60}^{o} with the Y-axis then \lambda is
  • 1\pm \sqrt{3}
  • 4\pm \sqrt{5}
  • 2\pm 2\sqrt{3}
  • 2\pm \sqrt{5}
The line joining the points (-2, 1, -8) and (a, b, c) is parallel to the line whose direction ratios are 6, 2, 3. The value of a, b, c are
  • (4, 3, -5)
  • (1, 2, -13/2)
  • (10, 5, -2)
  • (-5, 3, 4)
If a line has the direction ratio 18, 12, 4 , then its direction cosines are:
  • \dfrac{9}{11}, \dfrac{6}{11}, \dfrac{2}{11}
  • \dfrac{9}{13}, \dfrac{6}{13}, \dfrac{2}{13}
  • \dfrac{9}{7}, \dfrac{6}{7}, \dfrac{2}{7}
  • None of these
Equation of a line passing through the point \hat{i}+\hat{j}-\hat{k} and parallel to the vector 2\hat{i}+\hat{j}{+}2\hat{k} is
  • {\vec{r}}=(1+2{t})\hat{i}+(1+{t})\hat{j}{+}(1+2t)\hat{k}
  • {\vec{r}}=(1+2{t})\hat{i}+(1+{t})\hat{j}{+}(2{t}-1)\hat{k}
  • {\vec{r}}=(2{t}-1)\hat{i}+(1+{t})\hat{j}{+}(2{t}+1)\hat{k}
  • {\vec{r}}=(1-2{t})\hat{i}+(1+{t})\hat{i}{+}(2{t}+1)\hat{k}
A line with positive direction cosines passes through the point P(2, -1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals
  • 1
  • \sqrt{2}
  • \sqrt{3}
  • 2
Assertion (A): The points with position vectors \overline{a},\overline{b},\overline{c} are collinear if 2\overline{a}-7\overline{b}+5\overline{c}=0.
Reason (R): The points with position vectors \overline{a},\overline{b},\overline{c} are collinear if l\overline{a}+m\overline{b}+n\overline{c}=\overline{0}.
  • Both A and R are true and R is correct reason of A
  • Both A and R are true and R is not correct reason of A
  • A is true R is false
  • A is false R is true
If the points with position vectors 60\hat{i}+3\hat{j},40\hat{i}-8\hat{j} and a\hat{i}-52\hat{j} are collinear then a is equal to
  • -40
  • -20
  • 20
  • 40
The three points ABC have position vectors (1,x,3),(3,4,7) and (y,-2,-5) are collinear then (x,y)=
  • (2,-3)
  • (-2,3)
  • (-2,-3)
  • (2,3)
If \overline{a} and \overline{b} are two non-collinear vectors, then the points l_{1}\overline{a}+m_{1}\overline{b},  l_{2}\overline{a}+m_{2}\overline{b} and l_{3}\overline{a}+m_{3}\overline{b} are collinear if
  • \displaystyle \sum l_{1}(m_{2}-m_{3}) =0
  • \displaystyle \sum l_{1}(m_{1}-m_{3})=0
  • \displaystyle \sum l_{1}(m_{1}+m_{3})=0
  • \displaystyle \sum l_{1}(m_{2}+m_{3})=0
A line makes an angle \alpha,\beta,\gamma with the X,Y,Z axes. Then \sin^2\alpha+\sin^2\beta+\sin^2\gamma=
  • 1
  • 2
  • \dfrac 32
  • 4
The vectors 2\hat{i}+3\hat{j};5\hat{i}+6\hat{j};8\hat{i}+\lambda\hat{j} have their initial points at (1,1 ). The value of  \lambda so that the vectors terminate on one straight line is
  • 0
  • 3
  • 6
  • 9
The position vectors of three points are 2\overrightarrow { a } -\overrightarrow { b } +3\overrightarrow { c } ,\overrightarrow { a } -2\overrightarrow { b } +\lambda \overrightarrow { c } and \mu \overrightarrow { a } -5\overrightarrow { b } , where \overrightarrow { a } ,\overrightarrow { b } ,\overrightarrow { c } are non-coplanar vectors. The points are coliinear when
  • \displaystyle\lambda =-2,\mu =\frac { 9 }{ 4 }
  • \displaystyle\lambda =-\frac { 9 }{ 4 } ,\mu =2
  • \displaystyle\lambda =\frac { 9 }{ 4 } ,\mu =-2
  • None of these
The line passing through the points 10\hat{i}+3\hat{j}, 12\hat{i}+5\hat{j} also passes through the point a\hat{i}+11 \hat{j}, then a=
  • -8
  • 4
  • 18
  • 12
If the points (h, 3, -4), (0, -7, 10) and (1, k, 3) are collinear, then h + k is
  • 4
  • 0
  • -4
  • 14
The point collinear with (1, -2, -3) and (2, 0, 0) among the following is
  • (0,4,6)
  • (0,-4,-5)
  • (0, -4, -6)
  • (0,-4,6)
If the points whose position vectors are 2\overline{i}+\overline{j}+\overline{k},\ 6\overline{i}-\overline{j}+2\overline{k} and 14\overline{i}-5\overline{j}+p\overline{k} are collinear then the value of \mathrm{p} is
  • 2
  • 4
  • 6
  • 8
The points with position vectors \vec{a}+\vec{b},\vec{a}-\vec{b} and \vec{a}+\lambda\vec{b} are collinear for
  • Only integrals values of \lambda
  • No value of \lambda
  • All real values of \lambda
  • Only rational values of \lambda
If A = (1, 2, 3), B = (2, 10, 1), Q are collinear points and Q_x=-1, then Q_z=
  • -3
  • 7
  • -14
  • -7
If PQR are the three points with respective position vectors \hat{i}+\hat{j},\ \hat{i}-\hat{j} and a\hat{i}+b\hat{j}+c\hat{k}, then the points PQR are collinear if
  • a=b=c=1
  • a=b=c=0
  • a=1,\ b,c in R
  • a=1, c=0,\ b\in R
Find the angle between the two lines having direction ratio (1,1,2) and \left( \left( \sqrt { 3 } -1 \right) ,\left( -\sqrt { 3 } -1 \right) ,4 \right) .
  • \displaystyle \dfrac { \pi  }{ 3 }
  • \displaystyle \dfrac { \pi  }{ 2 }
  • \displaystyle \dfrac { \pi  }{ 6 }
  • None of these
The three points whose position vectors are \overline{i}+2\overline{j}+3\overline{k,} 3\overline{i}+4\overline{j}+7\overline{k,} and  -3\overline{i}-2\overline{j}-5\overline{k}
  • Form the vertices of an equilateral triangle
  • Form the vertices of an right angled triangle
  • Are collinear
  • Form the vertices of an isosceles triangle
Find the angle between the lines \overrightarrow { r } =3i+2j-4k+\lambda \left( i+2j+2k \right) and \overrightarrow { r } =\left( 5j-2k \right) +\mu \left( 3i+2j+6k \right)  
  • \displaystyle \theta =\cos ^{ -1 }{ \left( \frac { 19 }{ 21 }  \right)  }
  • \displaystyle \theta =\sin ^{ -1 }{ \left( \frac { 19 }{ 21 }  \right)  }
  • \displaystyle \theta =\cos ^{ -1 }{ \left( \frac { 20 }{ 21 }  \right)  }
  • None of these
If \vec{a},\vec{b},\vec{c} are the position vectors of points lie on a line, then \vec{a}\times \vec{b}+\vec{b}\times \vec{c}+\vec{c}\times \vec{a}=
  • 0
  • \vec{b}
  • 1
  • \vec{a}
The product of the d.r's of a line perpendicular to the plane passing through the points (4,0,0),(0,2,0) and ( 1,0,1) is
  • 6
  • 2
  • 0
  • 1
The d.r's of the line of intersection of the planes x+y+z-1 =0 and 2x+3y+4z-7 =0 are
  • 1, 2, -3
  • 2, 1, -3
  • 4, 2, -6
  • 1, -2, 1
The d.c's of the normal to the plane 2x-y+2z+5=0 are 
  • (3, -2, 6)
  • \left (\displaystyle \dfrac{2}{7},\dfrac{3}{7},\dfrac{-6}{7}\right)

  • \left (\displaystyle \dfrac{3}{7}\dfrac{-2}{7},\dfrac{6}{7}\right)

  • \left (\displaystyle \dfrac{2}{3}\dfrac{-1}{3},\dfrac{2}{3}\right)

The plane which passes through the point (-1, 0, -6) and perpendicular to the line whose direction ratios is (6, 20, -1) also passes through the point:
  • (1, 1, -26)
  • (0, 0, 0)
  • (2, 1, -32)
  • (1, 1, 1)
If R(a+2,a+3,a+4) divides the line segment joining P(2, 3, 4) and Q(4, 5, 6) in the ratio -3:2, then the value of the parameter which represents a is
  • 3
  • 2
  • 6
  • -1
lf the equation of the plane perpendicular to the \mathrm{z} -axis and passing through the point (2, -3,4) is ax+by+cz=d then \displaystyle \dfrac{a+b+c}{d}=
  • 4
  • \displaystyle \dfrac{3}{4}
  • 3
  • \displaystyle \dfrac{1}{4}
The equation to the plane bisecting the line segment joining (-3, 3, 2), (9, 5, 4) and perpendicular to the line segment is
  • x-y+4_{Z}-13=0
  • 2x-2y+7z-23=0
  • x-7y+2_{Z}-1=0
  • 6x+y+z-25=0
The direction ratios of a normal to the plane through (1,\ 0,\ 0),\ (0,\ 1,\ 0) which makes an angle of \displaystyle \dfrac{\pi}{4} with the plane x+y=3 are
  • 1,\ \sqrt{2},\ 1
  • 1,\ 1,\ \ \sqrt{2}
  • 1,\ 1,\ 2
  • \sqrt{2},\ 1,\ 1
Equation of the plane through the mid-point of the join of A(4,5,-10) and B(-1,2,1) and perpendicular to AB is
  • \vec{r}.(5i+3j-11k)+\dfrac{135}{2}=0
  • \vec{r}.(5i+3j-11k)=\dfrac{135}{2}
  • \vec{r}.\left (\dfrac{3}{2}\hat{i}+\dfrac{7}{2}\hat{j}-\dfrac{9}{2}\hat{k}\right)=5\hat{i}+3\hat{j}-11\hat{k}
  • \vec{r}.(5i+3j-11k)+\dfrac{185}{2}=0
If (2, 3, -1) is the foot of the perpendicular from (4, 2, 1) to a plane, then the equation of that plane is ax+by+cz=d. Then a+d is
  • 3
  • 1
  • -2
  • 2
The product of the d.cs of the line which makes equal angles with ox, oy, oz is
  • 1
  • \sqrt{3}
  • \displaystyle \dfrac{1}{3\sqrt{3}}
  • \displaystyle \dfrac{1}{\sqrt{3}}

lf \theta is the angle  between two lines whose d.cs are l_{1},m_{\mathrm{1}},n_{\mathrm{1}} and l_{2},m_{2},n_{2}, then

\displaystyle \dfrac{\Sigma(l_{1}+l_{2})^{2}}{4\cos^{2}(\dfrac{\theta}{2})}+\dfrac{\Sigma(l_{\mathrm{I}}-l_{2})^{2}}{4\sin^{2}(\dfrac{\theta}{2})}=

  • 1
  • 0
  • -1
  • 2
lf a line makes angles \displaystyle \dfrac{\pi}{12}, \displaystyle \dfrac{5\pi}{12} with OY, OZ  respectively where O=({0}, 0,0), then the angle made by that line with OX is
  • 45^{o}
  • 90^{o}
  • 60^{o}
  • 30^{\mathrm{o}}
The plane 2x+3y+kz-7=0 is parallel to the line whose direction ratios are (2, -3, 1), then k=
  • 5
  • 8
  • 1
  • 0
If the foot of the perpendicular from (0,0,0) to the plane is (1,2,2), then the equation of the plane is
  • -x+2y+8z-9=0
  • x+2y+2z-9=0
  • x+y+z-5=0
  • x+2y-3z+1=0
The sum of the squares of sine of the angles made by the line AB with OX, OY, OZ where O is the origin is
  • 1
  • 2
  • -1
  • 3
The direction ratios of a normal to the plane passing through (0,1,1), (1,1,2) and (-1,2,-2) are
  • (1,1,1)
  • (2,1,-1)
  • (1,2,-1)
  • (1,-2,-1)
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 12 Commerce Maths Quiz Questions and Answers