The shortest distance from the plane 12x + 4y + 3z = 327 to the s

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321.

The shortest distance from the plane 12x + 4y + 3z = 327 to the sphere x2 + y2 + z2 + 4x - 2y - 6z = 155,is

  • 26

  • 11413

  • 13

  • 39


A.

26

Given, equation of sphere isx2 + y2 + z2 + 4x - 2y - 6z - 155 = 0whose centre is (- 2, 1, 3)and radius = - 22 + 12 + 32 + 155                 = 4 + 1 + 9 + 155                 = 169 = 13 Required distance = distance of the plane from the centre of the sphere                = 12 × - 2 + 4 × 1 + 3 × 3 - 327122 + 42 × 32                = - 24 + 4 + 9 - 327144 + 16 + 9                = - 33813 = 33813 = 26


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322.

The acute angle between the line joining the points (2, 1, - 3), (- 3, 1, 7)and a line parallel to x - 13 = y4 = z + 35, through the point (- 1, 0, 4), is

  • cos-17510

  • cos-1110

  • cos-13510

  • cos-11510


323.

Two systems ofrectangular axis have the same origin. If a plane cuts them at distances a, b, c and d', b', c' from the origin, then

  • 1a2 + 1b2 + 1c2 + 1a'2 + 1b'2 + 1c'2 = 0

  • 1a2 + 1b2 - 1c2 + 1a'2 + 1b'2 - 1c'2 = 0

  • 1a2 - 1b2 - 1c2 + 1a'2 - 1b'2 - 1c'2 = 0

  • 1a2 + 1b2 + 1c2 - 1a'2 - 1b'2 - 1c'2 = 0


324.

If a plane passes through the point (1, 1, 1) and is perpendicular to the line x - 13 = y - 10 = z - 14 then its perpendicular distance from the origin is

  • 34

  • 43

  • 75

  • 1


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325.

The intersection of the spheres x2 + y2 + z2 + 7x - 2y - z = 13 and x2 + y2 + z2 - 3x + 3y + 4z = 8 is the same as the intersection of one of the sphere and the plane

  • x - y - z = 1

  • x - 2y - z = 1

  • x - y - 2z = 1

  • 2x - y - z = 1


326.

If θ is the angle between the vectors a = 2i^ + 2j^ - k^ and b = 6i^ - 3j^ + 2k^, then

  • cosθ = 421

  • cosθ = 319

  • cosθ = 219

  • cosθ = 521


327.

The ratio in which the xy-plane divides the join of (a, b, c) and (- a, - c, - b), is

  • a : b

  • b : c

  • c : a

  • c : b


328.

Lines x - 21 = y - 31 = z - 4- k and x - 1k = y - 42 = z - 51 will be coplanar, if

  • k = 0 or - 1

  • k = 1 or - 1

  • k = 0 or - 3

  • k = 3 or - 3


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329.

The equation of the plane containing the line

x - x1l = y - y1m = z - z1n is

a(x - x1) + b(y - y1) + c(z - z1) = 0, where

  • ax1 + by1 + cz1 = 0

  • al + bm + cn = 0

  • al + bm + cn

  • lx1 + my1 + nz1 = 0


330.

Distance between the is x - 13 = y + 2- 2 = z - 12 and the plane 2x + 2y - z = 6, is

 

  • 9 unit

  • 1 unit

  • 2 unit

  • 3 unit


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