In a quadrilateral ABCD, the point P divides DC in the ratio 1 :

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 Multiple Choice QuestionsMultiple Choice Questions

401.

If 3i^ + 3j^ + 3k^, 3i^ + 3j^ + λk^ are coplaner, then λ is equal to

  • 1

  • 2

  • 3

  • 4


402.

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

  • π4

  • π3

  • π2

  • 0


403.

If (2, - 1, 3) is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane is

  • 2x + y - 3z + 6 = 0

  • 2x - y + 3z - 14 = 0

  • 2x - y + 3z - 13 = 0

  • 2x + y + 3z - 10 = 0


404.

If the plane 3x - 2y - z - 18 = 0 meets the coordinate axes in A, B, C then the centroid of ABC is

  • (2, 3, - 6)

  • (2, - 3, 6)

  • (- 2, - 3, 6)

  • (2, - 3, - 6)


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405.

The direction cosines of the line passing through P(2, 3, - 1) and the origin are

  • 214, 314, 114

  • 214, - 314, 114

  • - 214, - 314, 114

  •  214, - 314, - 114


406.

If the direction cosines of two lines are such that l + m + n = 0, l2 + m2 - n2 = 0, then the angle between them is :

  • π

  • π3

  • π4

  • π6


407.

The ratio in which yz-plane divides the line segment joining ( - 3, 4, - 2) and (2, 1, 3) is

  • - 4 : 1

  • 3 : 2

  • - 2 : 3

  • 1 :4


408.

The cosine of the angle A of the tnangle with vertices

A(1, - 1, 2), B(6, 11, 2), C(1, 2, 6) is

  • 6365

  • 3665

  • 1665

  • 1364


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409.

The angle between the lines whose direction 

cosine are 34, 14, 32 and 34, 14, - 32, is

  • π

  • π2

  • π3

  • π4


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410.

In a quadrilateral ABCD, the point P divides DC in the ratio 1 : 2 and Q is the mid point of AC. IfAB + 2AD + BC - 2DC = kPQ, then k is equal

  • - 6

  • - 4

  • 6

  • 4


A.

- 6

Now, AB + 2AD + BC - 2DC = AC  + 2AD - 2DC                                                   = AC  + 2AC + CD - 2DC

= 3AC - 4DC= 32QC - 432PC= 6QC - 6PC = 6QC + CP kPQ =  6QP = - 6PQ     Given k = - 6


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