A point on XOZ - plane divides the join of (5, - 3, - 2) and (1,

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 Multiple Choice QuestionsMultiple Choice Questions

231.

If I is incentre of ABC, then I is

  • aa +bb +cca +b +c

  • aa +bb +cca2 +b2 +c2

  • 13a + b + c

  • a +b + ca +b +c


232.

What are the DR's of vector parallel to (2, - 1, 1) and (3 4, - 1) ?

  • (1, 5, - 2)

  • (- 2, - 5, 2)

  • (- 1, 5, 2)

  • (- 1, - 5, - 2)


233.

Let ABCD be a parallelogram whose diagonals intersect at P and O be the origin, then OA + OB + OC + OD

  • OP

  • 2OP

  • 3OP

  • 4OP


234.

A unit vector in the plane of i^ +2j^ +k^ and i^ +j^ +2k^ and perpendicular to 2i^ +j^ +k^, is

  • j^ -k^

  • i^ +j^2

  • j^ +k^2

  • j^ -k^2


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235.

The line joining the points 6a - 4b + 4c, - 4c and the line joining the points - a - 2b - 3c, a + 2b - 5c intersect at

  • - 4a

  • 4a - b - c

  • 4c

  • None of the above


236.

The symmetric equation of lines 3x + 2y + z - 5 = 0 and x + y - 2z - 3 = 0, is

  • x - 15 = y - 47 = z - 01

  • x + 15 = y + 47 = z - 01

  • x + 1- 5 = y - 47 = z - 01

  • x - 1- 5 = y - 47 = z - 01

     


237.

The equation of the plane containing the line x + 1- 3 = y - 32 = z + 21 and the point (0, 7, - 7) is

  • x + y + z = 1

  • x + y + z = 2

  • x + y + z = 0

  • None of these


238.

Angle of intersection of the curve r = sinθ + cosθ and r = 2sinθ is equal to

  • π2

  • π3

  • π4

  • None of these


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239.

A point on XOZ - plane divides the join of (5, - 3, - 2) and (1, 2, - 2) at

  • 135, 0, - 2

  • 135, 0, 2

  • (5, 0, 2)

  • (5, 0, - 2)


A.

135, 0, - 2

Let point P(x, y, z) divides the line joining the points A and B in the ratio m : 1.

Since, point P is on XOZ-plane

 y coordinate= 0 2m - 3m + 1 = 0           m = 32Now, x = 3 + 2 × 53 + 2 = 135and z = 3 × - 2 + 2 × - 25 = - 2 Required point is 135, 0, - 2


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240.

If the line OR makes angles θ1, θ2, θ3, with the planes XOY, YOZ, ZOX respectively, then cos2θ1 + cos2θ2 + cos2θ3, is equal to

  • 1

  • 2

  • 3

  • 4


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