Let A(1, - 1, 2) and B (2, 3, - 1) be two points. If a point P di

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

31.

If the vectors a = 2i^ + j^ + 4k^, b = 4i^ - 2j^ + 3k^ and c = 2i^ - 3j^ - λk^ are coplanar, then the value of λ is equal to

  • 2

  • 1

  • 3

  • - 1


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32.

Let A(1, - 1, 2) and B (2, 3, - 1) be two points. If a point P divides AB internally in the ratio 2 : 3, then the position vector of P is

  • 15i^ + j^ + k^

  • 13i^ +  6j^ + k^

  • 13i^ + j^ + k^

  • 157i^ + 3j^ + 4k^


D.

157i^ + 3j^ + 4k^

The position vector of P

= 3A +2B3 +2= 31, - 1, 2 + 22, 3, - 15= 7, 3, 45

= 157i^ + 3j^ + 4k^


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33.

If the scalar product of the vector i^ + j^ + 2k^ with the unit vector along mi^ + 2j^ + 3k^ is equal to 2, then one of the values of m is

  • 3

  • 4

  • 5

  • 6


34.

A plane makes intercepts a, b, cat A, B, C on the coordinate axes respectively. If the centroid of the ABC is at (3, 2, 1), then the equation of the plane is

  • x + 2y + 3z = 9

  • 2x - 3y - 6z = 18

  • 2x + 3y + 6z = 18

  • 2x + y + 6z = 18


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35.

If the plane 3x + y + 2z + 6 = 0 is parallel to the line 3x - 12b = 3 - y = z - 1a, then the avlue of 3a + 3b is

  • 12

  • 32

  • 3

  • 4


36.

The equation of the line passing through the point (3, 0,- 4) and perpendicular to the plane 2x - 3y + 5z - 7 = 0 is

  • x - 23 = y- 3 = z + 45

  • x - 32 = y- 3 = z - 45

  • x - 23 = - y3 = z + 45

  • x + 32 = y3 = z - 45


37.

The plane r = si^ + j^ - 4k^ + t3i^ +4 j^ - 4k^ + 1 - t2i^ - 7j^ - 3k^ is parallel to the line

  • r = - i^ + j^ - k^ + t- i^ - 2j^ + 4k^

  • r = - i^ + j^ - k^ + t i^ - 2j^ + 4k^

  • r = i^ + j^ - k^ + t- i^ - 4j^ + 7k^

  • r = - i^ + j^ - 3k^ + t2i^ + 6j^ - 8k^


38.

The distance between the line r = 2i^ + 2j^ - k^ + λ2i^ + j^ - 2k^ and the plane r . i^ + 2j^ + 2k^ = 10 is equal to

  • 5

  • 4

  • 3

  • 2


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39.

Equation of the plane passing through t intersection of the planes x + y + z = 6 and 2x + 3y + 4z + 5 = 0 and the point (1, 1, 1)

  • 20x + 23y + 26z - 69 = 0

  • 31x + 45y + 49z + 52 = 0

  • 8x + 5y + 2z - 69 = 0

  • 4x + 5y + 6z - 7 = 0


40.

The equation of the plane containing the line x - 12 = y + 1- 1 = z3 and x2 = y - 2- 1 = z + 13 is

  • 8x - y + 5z - 8 = 0

  • 8x + y - 5z - 7 = 0

  • x - 8y + 3z + 6 = 0

  • 8x + y - 5z + 7 = 0


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