A plane makes intercepts 3 and 4 respectively on Z-axis and X-axi

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 Multiple Choice QuestionsMultiple Choice Questions

391.

If P = (0, 1, 0), Q = (0, 1, 0), then the projection of PQ on the plane x + y + z = 3 is

  • 2

  • 2

  • 3

  • 3


392.

In the space the equation by + cz + d = 0 represents a plane perpendicular to the

  • YOZ-plane

  • ZOX-plane

  • XOY-plane

  • None of these


393.

A plane x passes through the point (1, 1, 1). If b, c, a are the direction ratios of a normal to the plane, where a, b, c (a < b < c) are the factors of 2001, then the equation of plane is 

  • 29x + 31y + 3z = 63

  • 23x + 29y - 29z = 23

  • 23x + 29y + 3z = 55

  • 31x + 37y + 3z = 71


394.

If the plane 7x + 11y + 13z = 3003 meets the co-ordinate axes in A, B, C, then the centroid of the ABC is

  • (143, 91, 77)

  • (143, 77, 91)

  • (91, 143, 77)

  • (143, 66, 91)


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395.

If a,b, c are three non-coplanar vectors, then the vector equation r = 1 - p - qa + pb + qc represents a :

  • straight line

  • plane

  • plane apssing through origin

  • sphere


396.

If a,b, c are three vectors such that a = b + c and the angle between b and c is π2, then

  • a2 = b2 + c2

  • b2 = c2 + a2

  • c2 = a2 + b2

  • 2a2 - b2 = c2


397.

XOZ-plane divides the join of (2, 3, 1) and(6, 7, 1) in the ratio :

  • 3 : 7

  • 2 : 7

  • - 3 : 7

  • - 2 : 7


398.

If the direction ratio of two lines are given by 3lm - 4ln + mn = 0 and l + 2m + 3n = 0, then the angle between the lines, is :

  • π6

  • π4

  • π3

  • π2


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399.

A plane makes intercepts 3 and 4 respectively on Z-axis and X-axis. If it is parallel to Y-axis, then its equation is

  • 3x + 4z = 12

  • 3z + 4x = 12

  • 3y + 4z = 12

  • 3z + 4y = 12


A.

3x + 4z = 12

Given that a = 4, c= 3Equation of the plane 'π' isxa + yb + zc = 1  x4 + yb + zc = 1Since, π is parallel to y - axis0 1a + 1 1b + 0 1c1a2 + 1b2 + 1c2 = 0  1b = 0Thus, the equation of plane π isx4 + z3 = 1  3x + 4z - 12 = 0


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400.

The equation of the plane passing through(1, 1, 1) and   (1, - 1, - 1) and perpendicular to 2x -y + z = 0 is :

  • 2x +5y +z + 8 = 0

  • x + y - z - 1 = 0

  • 2x + 5y + z + 4 = 0

  • x - y + z - 1 = 0


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