Image point of (1, 3, 4) in the plane 2x - y + z + 3 = 0 will be

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 Multiple Choice QuestionsMultiple Choice Questions

371.

If A(- 1, 3, 2),B (2, 3, 5) and C(3, 5, - 2) are vertices of a ABC, then angles of ABC are

  • A = 90°, B = 30°, C = 60°

  • A = B = C = 90°

  • A = B = 45°, C = 90°

  • None of the above


372.

If a, band care three non-coplanar vectors, then [a x b b x c c x a] is equal to

  • [a b c]3

  • [a b c]2

  • 0

  • None of these


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373.

Image point of (1, 3, 4) in the plane 2x - y + z + 3 = 0 will be

  • (3, 5, 2)

  • (3, 5, - 2)

  • (- 3, 5, 2)

  • None of these


C.

(- 3, 5, 2)

Since, image of a point (x, y, z,) in the plane ax + by + cz + d = 0 is

x - x1a = y - y1b = z - z1c    = - 2ax1 + by1 + cz1 + da2 + b2 + c2So, image of point(1, 3, 4) in the plane2x - y +z+ 3 = 0 isx - 12 = y - 3- 1 = z - 41 = - 2    x = 1 - 4, y = 3 + 2, z = - 2 + 4    x = - 3, y = 5, z = 2i.e., required points (- 3, 5, 2).


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374.

Distance of the point (2, 3, 4) from the plane 3x - 6 y + 2z + 11 = 0 is

  • 0

  • 1

  • 2

  • 3


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375.

The three lines of a triangle are given by (x2 - y2)(2x + 3y - 6) = 0. If the point (- 2, λ) lies inside and (μ, 1) lies outside the triangle, then

  • λ  1, 103, μ  - 3, 5

  • λ  2, 103, μ  - 1, 1

  • λ  - 1, 92, μ  - 2, 103

  • None of the above


376.

A variable plane is at a constant distance p from the origin O and meets the axes at A, B and C. The locus of the centroid of the tetrahedron OABC is

  • 1x2 + 1y2 + 1z2 = 1p2

  • 1x2 + 1y2 + 1z2 = 16p2

  • x2 + y2 + z2 = 16p2

  • x2 + y2 + z2 = p2


377.

The equation of the plane through intersection of planes x + 2y + 3z = 4 and 2x + y - z = - 5 and perpendicular to the plane 5x + 3y + 6z = - 8 is

  • 23x + 14y - 9z = - 8

  • 51x + 15y - 50z = - 173

  • 7x - 2y + 3z = - 81

  • None of the above


378.

If l, m, n are the direction cosines of a line, then the maximum value of lmn is

  • 123

  • 153

  • 13

  • None of the above


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379.

If the shortest distance between the lines x - 12 = y - 23 = z - 34 and x - 23 = y - 44 = z - 55 is d, then [d], where [.] is the greatest integer function, is equal to

  • 0

  • 1

  • 2

  • 3


380.

The angle between the planes 3x-  4y + 5z = 0 and 2x - y - 2z = 5 is

  • π6

  • π3

  • π2

  • None of these


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