JEE Questions for Maths Three Dimensional Geometry Quiz 7

The plane ax + by + cz = 1meets the coordinates axes at A, B and C. The centroid of ∆ABC is

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(3a, 3b, 3c)
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2)
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(a, b, c)

If the distance of the point P(1, -2,from the plane x + 2y - 2z = a, where a > 0, is 5, then the foot of the perpendicular from P to the plane is

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2)
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Statement I The point A(3, 1,is the mirror image of the point P(1, 3,in the plane x - y + z = 5.
Statement II The plane x - y + z = 5 bisects the line segment joining A(3, 1,and B(1, 3, 4).

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Statement I is correct, Statement II is correct; Statement II is correct explanation for Statement I
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Statement I is correct, Statement II is correct; Statement II is not correct explanation for Statement I
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Statement I is correct, Statement II is incorrect
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Statement I is incorrect, Statement II is correct

The intercepts of the plane 2x - 3y + 4z = 12 on the coordinate axes are given by

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3, -2, 15
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6, -4, 3
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6, -4, -3
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2, -3, 4

The distance of the plane 6x - 3y + 2z - 14 = 0 from the origin is

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2
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1
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14
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8

If the planes x = cy + bz, y = az + cx, z = bx + ay pass through a line, then a² + b² + c² + 2abc is

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0
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1
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2
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3

The angle between two planes 2x - y + z = 6 and x + 2y + 3z = 3 is

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2)
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A plane makes intercepts (-6, 3,upon the coordinate axes. Then, the length of the perpendicular from the origin on it is

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2/√29
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3/√29
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4/√29
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12/√29

Let L be the line of intersection of the planes 2x + 3y + z = 1 and x + 3y + 2z = 2. If L makes an angle α with the positive X - axis, then cos α equals

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1/√3
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1/2
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1
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1/√2

If from a point P(a, b, c), perpendicular PA and PB are drawn to YZ and ZX-planes, then the equation of the plane OAB is

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bcx + cay + abz = 0
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bcx + cay - abz = 0
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bcx - cay + abz = 0
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-bcx + cay + abz = 0
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ax + by + cz = 0

If the planes x + 2y + kz = 0 and 2x + y - 2z = 0 are at right angles, then the value of k is

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2
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-2
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1/2
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-1/2

Equation of the plane parallel to the planes x + 2y + 3z - 5 = 0, x + 2y + 3z - 7 = 0 and equidistant from them is

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x + 2y + 3z - 6 = 0
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x + 2y + 3z - 1 = 0
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x + 2y + 3z - 8 = 0
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x + 2y + 3z - 3 = 0
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x + 2y + 3 - 10 = 0

The equation of the plane, which makes with coordinate axes, a triangle with its centroid (α, β, γ) is

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αx + βy + γz = 3
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αx + βy + γz = 1
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Maths-Three Dimensional Geometry-52987.png

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9
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3
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1/9
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1/3

If for a plane, the intercepts on the coordinate axes are 8, 4 and 4, then the length of the perpendicular from the origin on the plane is

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8/3
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3/8
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3
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4/3
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4/5

A plane which passes through the point (3, 2,and the line (x - 4)/1 = (y - 7)/5 = (z - 4)/4 is

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x + y + z = 1
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x + 2y - z = 1
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x - y + z = 1
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2x - y + z = 5

Maths-Three Dimensional Geometry-52989.png

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2)
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Maths-Three Dimensional Geometry-52994.png

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A = 3, B = 2, C = 4, D = 1
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A = 1, B = 3, C = 4, D = 2
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A = 3, B = 2, C = 1, D = 4
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A = 2, B = 4, C = 1, D = 3

Maths-Three Dimensional Geometry-52995.png

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-1
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2/9
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9/2
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0

The equation of the perpendicular from the point (α, β, γ) to the plane ax + by + cz + d = 0 is

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2)
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Maths-Three Dimensional Geometry-53000.png

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8x - y + 5z - 8 = 0
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8x + y - 5z - 7 = 0
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x - 8y + 3z + 6 = 0
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8x + y - 5z + 7 = 0
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x + y + z - 6 = 0

The equation of the line passing through the point (3, 0, -and perpendicular to the plane 2x - 3y + 5z - 7 = 0 is

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2)
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Maths-Three Dimensional Geometry-53006.png

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2
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3
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6
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7

A line with positive direction cosines passes through the point P(2, -1,and makes equal angles with the coordinates axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals