Loading [MathJax]/jax/output/CommonHTML/jax.js

CBSE Questions for Class 12 Commerce Maths Three Dimensional Geometry Quiz 11 - MCQExams.com

If AB=21, B(2,1,8) and the direction cosines of AB are 67,27,37 then the coordinates of A are
  • (16,7,1)
  • (20,5,17)
  • (16,7,1)
  • (20,5,17)
The direction ratios of the normal to the plane through (1,0,0) and (0,1,0) which makes an angle of π4 with the plane x+y=3 are-
  • 1,2,1
  • 1,1,2
  • 1,1,2
  • 2,1,1
If l1,m1,n1 and l2,m2,n2 are the d.c.s of the two lines, then (l1l2+m1m2+n1n2)2+(l1m2l2m1)2+(m1n2m2n1)2+(n1l2n2l1)2=
  • 3
  • 2
  • 1
  • 4
If P=(0,1,2),Q=(4,2,1),O=(0,0,0) then POQ=
  • π6
  • π4
  • π3
  • π2
If a line makes angles α,β,γ with positive axes, then the range of sinαsinβ+sinβsinγ+sinγsinα is
  • (12,1)
  • (12,2)
  • (1,2)
  • (1,2]
If the angle between the lines, x2=y2=z1 and 5x2=7y14P=z34 is cos1(23), then p is equal to: 
  • 47
  • 72
  • 74
  • 27
The direction cosines of the line which is perpendicular to the lines whose direction cosines are proportional to ( 1, -1,2 ) and ( 2,1,-1) are:- 
  • 135,535,335
  • 135,535,335
  • 135,535,335
  • none of these
If (2,1,3) and (1,2,4) are the extermities of a diagonal of a rhombus then the d.rs of the other diagonal are
  • (2,3,9)
  • (2,3,9)
  • (1,2,4)
  • (2,3,1)
The direction cosines of the line which is perpendicular to the lines whose direction cosines are proportional to (1,1,2) and (2,1,1) are
  • 135,535,335
  • 1335,135,135
  • 23,53,73
  • 335,535,735
A mirror and source of light are kept at the origin and the positive x-axis respectively a ray a light from the sources strikes the mirror and is reflected. If (1,-1,1) are the Dr's of a normal to the plane. Then the D.C's of the reflected ray are 
  • (13,23,23)
  • (13,23,23)
  • (13,23,23)
  • (13,23,23)
If the incident ray and normal have the directions of the vectors (1,3,1),(1,1,1) respectively, then direction of the reflected ray is-
  • (4,8,4)
  • (5,7,5)
  • (6,6,6)
  • (5,7,5)
The direction cosines of the line which is perpendicular to the lines whose direction cosines are proportional to (1,-1,2) and (2,1,-1) are:- 
  • 135,535,335
  • 135,535,335
  • 135,535,335
  • None of these
If from the point P(f,g,h) perpendiculars PL,PM be drawn to yz and zx planes then the equation to the plane OLM is -
  • xf+yg+zh=0
  • xf+ygzh=0
  • xf+yg+zh=0
  • xfyg+zh=0
The equation of the plane passing through (1,1,1) and (1,1,1) and perpendicular to 2xy+z+5=0 is
  • 2x+5y+z8=0
  • x+yz1=0
  • 2x+5y+z+4=0
  • xy+z1=0
The direction ratios of two lines are (4,3,5) and (λ,1,2). If the angle between them is 45o, a value of λ is
  • 0
  • 2
  • 3
  • 1
The st lines whose direction cosines satisfy:
al+bm+cn=0 and fmn+gnl+hlm=0 are perpendicular if: 
  • fa+gb+hc=0
  • a2f+b2g+c2h=0
  • af+bg+ch=0
  • a2f+b2g+c2h=0.
If l1, m1, n1 and l2, m2, n2 are the direction cosines of two perpendicular lines, then the direction cosine of the line which is perpendicular to both the lines , will be
  • (m1n2 - m2n1), (n1l2 - n2l1), (l1m2 - l2m1)
  • (l1l2 - m1m2), (m1m2 - n1n2), (n1n2 - l1l2)
  • 1l21+m21+n21, 1l22+m22+n22, 13
  • 13, 13, 13
If two straight lines having directions cosines λ,m,n and f,g,h satisfy λ+m+n=0 and fmn+gnλ+hλm=0 and are perpendicular then f+g+h is equal to
  • 0
  • 1
  • 1
  • 2
The Dr's of two lines are 1, -2, -2 and 0, 2, 1 the Dc's of the line perpendicular to the above lines are :-
  • 23,13,23
  • 13,23,23
  • 114,34,23
  • None of these
In a plane there are 10 points, no three are in same straight line except 4 points which are collinear, then the number of straight lines are
  • 39
  • 41
  • 45
  • 40
The point collinder with (1,-2,-3) and (2,0,0) amoung the following is 
  • (0,4,6)
  • (0, -4, -5)
  • (0, -4, -6)
  • non of these
A line with direction ratio 2,7,-5 is drawn to intersect the lines xy3=y71=z+21 and x+33=y32=z64 at P and Q respectively, then length of PQ is-
  • 78
  • 77
  • 54
  • 74
L1 and L2 are two lines whose vector equations are L1:r=λ[(cosθ+3)ˆi+(2sinθ)ˆj+(cosθ3)ˆk]
L2:r=μ(aˆi+bˆj+cˆk), whereλ and μ are scalars andα is the acute angle between L1andL2 If the angleα is independent of θ then the value of α is
  • π6
  • π4
  • π3
  • π2
Direction ratio of two lines are l1,m1,n1 and  l2,m2,n2 then direction ratios of the line perpendicular to both the lines are
  • l1l2,m1m2,n1n2
  • l1+l2,m1+m2,n1+n2
  • m1n2n1m2,n1l2n2l1,l1m2m1l2
  • m1n2n1m2,n1l2n1l1,l1m2m1l2
The equation to the altitude of the triangle formed by (1,1,1), (1,2,3), (2,1,1) through (1,1,1).
  • ˉr=(ˉi+ˉj+ˉk)+t(ˉi3ˉj2ˉk)
  • ˉr=(ˉi+ˉj+ˉk)+t(3ˉi+ˉj+2ˉk)
  • ˉr=(ˉi+ˉj+ˉk)+t(ˉiˉj+2ˉk)
  • |ˉr|=5
The plane passing through (1,1,1),(1,1,1) and (7,3,5) is parallel to 
  • Xaxis.
  • Yaxis.
  • Zaxis.
  • None of these
Each group from the alternatives represents lengths of sides of a triangleStare which group does not represent a right-angled triangle.
  • (8,40,41)
  • (20,25,30)
  • (8,15,17)
  • (6,8,10)
there are 20 points in the plane on three of which are collinear. the number of straight lines by joining them is
  • 190
  • 200
  • 40
  • 500
The lines r=ij+λ(2i+k) and r=(2ij)+μ(i+jk) intersect for
  • λ=1,μ=1
  • λ=2,μ=1
  • All values of λ and μ
  • No value of λ and μ
The value of p so that the lines 1x3=7y142p=z32 and 77x3p=y51=6z5 are at right angles are
  • 70/11
  • 7/11
  • 10/7
  • 17/11
What is the area of the triangle with vertices (0,2,2),(2,0,1) and (3,4,0) ?
  • 152sq unit
  • 15sq unit
  • 72sq unit
  • 7sq unit
In the three points with position vectors (1, a. b) : (a, b, 3) are collinear in space, then the value of a + b is 
  • 3
  • 4
  • 5
  • none
The number of straight lines that can be drawn through any two points out of 10 points, of which 7 are collinear.
  • 25
  • 30
  • 35
  • 45
If the vectors 2ˆi+3ˆj, 5ˆi+6ˆj, and 8ˆi+λˆj have their initial points at (1,1), then the value of λ so that the vectors terminate on one straight line is
  • 0
  • 3
  • 6
  • 9
If  (0,0),(a,0)  and  (0,b)  are collinear, then
  • ab=0
  • a=b
  • a=b
  • ab=c
If points (a2,a4);(a,a+1) and (a+4,16) are collinear, then a is equal to
  • 5
  • 5
  • 7
  • 7
The direction cosines of the normal to the plane 2xy+2z=3 are 
  • 23,13,23
  • 23,13,23
  • 23,13,23
  • 23,13,23
The plane passing through the point (5,1,2) perpendicular to the line 2(x2)=y4=z5 will meet the line in the point
  • (1,2,3)
  • (2,3,1)
  • (1,3,2)
  • (3,2,1)
The equation of the plane passing through the points (3,2,1),(3,4,2) and (7,0,6) is 5x+3y2z=λ where λ is
  • 23
  • 21
  • 19
  • 27
The vector equation of line 2x - 1 = 3 y + 2 = z - 2 is 
  • ˉr=(12ˆi23ˆj+2ˆk)+λ(3ˆi+2ˆj+6ˆk)
  • ˉr=ˆi>j+(2ˆi+ˆj+ˆk)
  • ˉr=(12ˆiˆj)+λ(ˆi+2ˆj+6ˆk)
  • ˉr=(ˆi+ˆj)+λ(ˆi2ˆj+6ˆk)
If P, Q  R are collinear points such that P( 7, 7) Q( 3, 4) and PR = 10 then R is 
  • (1, 1)
  • ( 1, -1)
  • ( -1, 1)
  • ( -1, -1)
0:0:2


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 12 Commerce Maths Quiz Questions and Answers