The equation of the plane through the line of intersection of the

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141.

The equation of the plane through the line of intersection of the planes x - y + z + 3 = 0 and x + y + 22 + 1 = 0 and parallel to x-axis is

  • 2y - z = 2

  • 2y + z = 2

  • 4y + z = 4

  • y - 2z = 3


B.

2y + z = 2

The intersection equation of planes x - y + z + 3 = 0 and x + y + 2z + 1 = 0 is (x - y + z + 3) + λ(x + y + 2z + 1) = 0

 1 + λx + - 1 + λy + 1 + 2λz + 3 + λ = 0DR's of x - axis is (1, 0, 0)Since, above plane is parallel to x-axis  Coefficient of x = 01 - λ = 0   λ = - 1 1 - 1x + - 1 - 1y + 1 - 2z + 3 - 1 = 0 0 - 2y - z + 2 = 0                2y + z = 2


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142.

If 3p + 2q = i + j + k and 3p - 2q = i - j - k, then the angle between p and q is

  • π6

  • π4

  • π3

  • π2

     


143.

The point of intersection of the straight line x - 22 = y - 1- 3 = z + 21 with the plane x + 3y - z + 1 = 0 is

  • (3, - 1, 1)

  • (- 5, 1, - 1)

  • (2, 0, 3)

  • (4, - 2, - 1)


144.

If the lines 2x - 12 = 3 - y1 = z - 13 and x + 32 = z + 1p = y + 25 are perpendicular to each other, then p is equal to

  • 1

  • - 1

  • 10

  • 75


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145.

The point P(x, y, z) lies in the first octant and its distance from the origin is 12 units. If the position vector of P make 45° and 60° with the x-axis and y-axis respectively, then the coordinates of P are

  • 33, 6, 32

  • 43, 8, 42

  • 62, 6, 6

  • 6, 6, 62


146.

The distance between the planes r . (i + 2j - 2k) + 5 = 0 and r . (2i + 4j - 4k) - 16 = 0 is

  • 3

  • 113

  • 13

  • 133


147.

If the angle θ between the line x + 11 = y - 12 = z - 22 and the plane 2x - y + pz + 4 = 0 is such that sinθ = 13, then the value of p is

  • 0

  • 13

  • 23

  • 53


148.

The ratio in which the plane y - 1 = 0 divides the straight line joining (1, - 1, 3) and (- 2, 5, 4) is

  • 1 : 2

  • 3 : 1

  • 5 : 2

  • 1 : 3


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149.

Equation of the line passing through i + j - 3k and perpendicular to the plane 2x - 4y + 3z + 5 = 0 is

  • x - 12 = 1 - y- 4 = z - 33

  • x - 12 = 1 - y4 = z + 33

  • x - 21 = y + 41 = z - 33

  • x - 1- 2 = 1 - y- 4 = z - 33


150.

The angle between the straight lines x - 1 = 2y + 33 = z +52 and x = 3r + 2; y = - 2r - 1; z = 2, where r is a parameter, is

  • π4

  • cos-1- 3182

  • sin-1- 3182

  • π2


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