If the origin and the points P(2, 3, 4 ), Q(1, 2, 3) and R(x, y,

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 Multiple Choice QuestionsMultiple Choice Questions

251.

The angle between a line with direction ratio 2 : 2 : 1 and a line joining (3, 1, 4) to (7, 2, 12) is

  • cos-123

  • cos-132

  • tan-1- 23

  • None of the above


252.

If a + b + c = 0 and a = 5, b = 3 and c = 7, then angle between a and b is

  • π2

  • π3

  • π4

  • π6


253.

Direction cosines of the line x + 22 = 2y - 53, z = - 1 are

  • 45, 35, 0

  • 35, 45, 15

  • - 35, 45, 0

  • 45, - 25, 15


254.

The acute angle between the line r = i^ + 2j^ + k^ + λi^ + j^ + k^ and the plane 2i^ - j^ + k^ = 5

  • cos-123

  • sin-123

  • tan-123

  • sin-123


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255.

If A and B are foot of perpendicular drawn from point Q(a, b, c) to the planes yz and zx, then equation of plane through the points A, B and O is

  • xa + yb - zc = 0

  • xa - yb + zc = 0

  • xa - yb - zc = 0

  • xa + yb + zc = 0


256.

If line joining points A and B having position vectors 6a - 4b + 4c and - 4c respectively and the line joining the points C and 0 having position vectors - a - 2b - 3c and a + 2b - 5c intersect, then point of intersection is

  • B

  • C

  • D

  • A


257.

Direction ratios of the line which is perpendicular to the lines with direction ratios - 1, 2, 2 and 0, 2, 1 are

  • 1, 1, 2

  • 2, - 1, 2

  • - 2, 1, 2

  • 2, 1, - 2


258.

If the angle between the planes r . mi^ - j^ + 2k^ + 3 = 0 and r . 2i^ - mj^ - k^ - 5 = 0 is π3, then m =

  • 2

  • ± 3

  • 3

  • - 2


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259.

If the origin and the points P(2, 3, 4 ), Q(1, 2, 3) and R(x, y, z) are coplanar, then

  • x - 2y - z = 0

  • x + 2y + z = 0

  • x - 2y + z = 0

  • 2x - 2y + z = 0


C.

x - 2y + z = 0

Let O(0, 0, 0) be the origin.

It is given that O(0, 0, 0), P(2, 3, 4), Q(1, 2, 3) and R (x, y, z) are coplanar.

 OR OP OQ

x - 0y - 0z - 02 - 03 - 04 - 01 - 02 - 03 - 0 = 0                      xyz234123 = 0 x9 - 8 - y6 - 4 + z4 - 3 = 0                                   x - 2y + z = 0


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260.

If lines represented by equation px2 - qy2 = 0 are distinct, then

  • pq > 0

  • pq < 0

  • pq = 0

  • p + q = 0


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