The distance between the line r→ = 2i^ +

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 Multiple Choice QuestionsMultiple Choice Questions

111.

If the lines 1 - x3 = y - 22α = z - 32x - 13α = y - 1 = 6 - z5 are perpendicular, then the value of α is

  • - 107

  • 107

  • - 1011

  • 1011


112.

The distance between the lines r = 4i^ - 7j^ - 9k^ + t3i^ - 7j^ + 4k^ and r = 7i^ - 14j^ - 5k^ + s- 3i^ + 7j^ - 4k^ is equal to

  • 1

  • 12

  • 34

  • 0


113.

Let Tn denote the number of triangles which can equal to be formed by using the vertices of a regular polygon of n sides. If Tn + 1 - Tn = 28, then n equals

  • 4

  • 5

  • 6

  • 8


114.

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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115.

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


116.

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


117.

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^


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118.

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


D.

2

The given line is

r = 2i^ + 2j^ - k^ + λ2i^ + j^ - 2k^or r = a + λbwhere a = 2i^ + 2j^ - k^,and     b = 2i^ + j^ - 2k^The equation of plane isr . i^ + 2j^ + 2k^ = 10or r . n = dwhere n = i^ + 2j^ + 2k^Since, b . n = 2i^ + j^ - 2k^ . i^ + 2j^ + 2k^                      = 2 + 2 - 4 =  0

Therefore, the line is parallel to the plane.

Hence, the required distance

= 2i^ + j^ - 2k^ . i^ + 2j^ + 2k^ - 101 + 4 + 4= 2 + 4 - 2 - 109= - 63 = 2


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119.

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


120.

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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