If a,b, c are three vectors such that a→ = b&

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 Multiple Choice QuestionsMultiple Choice Questions

721.

If P = (0, 1, 2), Q =(4, - 2, 1), O =(0, 0, 0), then POQ is equal to

  • π2

  • π4

  • π6

  • π3


722.

A variable plane is at a constant distance h from the origin and meets the coordinate axes in A, B, C. Locus of centroid of ABC is

  • x2 + y2 + z2 = h- 2

  • x2 + y2 + z2 = 4h- 2

  • x2 + y2 + z2 = 16h2

  • 1x2 + 1y2 + 1z2 = 9h2


723.

The acute angle between the two lines whose direction ratios are given by l + m - n = 0 and  l2 + m2 + n2 = 0, is

  • 0

  • π6

  • π4

  • π3


724.

The direction ratios of normal to the plane passing through (0, 0, 1), (0, 1, 2) and (1, 0, 3) are

  • (2, 1, - 1)

  • (1, 0, 1)

  • (0, 0, - 1)

  • (1, 0, 0)


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725.

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


726.

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

  • YOZ-plane

  • ZOX-plane

  • XOY-plane

  • None of these


727.

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


728.

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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729.

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


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730.

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


A.

a2 = b2 + c2

Given that, a = b + c

and b  cthen, a2 = b2 + c2            a2 = b2 + c2


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