The distance of the point (- 2, 4, - 5) from the line x 

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 Multiple Choice QuestionsMultiple Choice Questions

311.

Reflexion of the point α, β, γ in XY-plane is

  • 0, 0, γ

  • - α, - β, γ

  • α, β, - γ

  • α, β, 0


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312.

The distance of the point (- 2, 4, - 5) from the line x + 33 = y - 45 = z + 86 is

  • 3710

  • 3710

  • 3710

  • 3710


A.

3710

The line passes through A(- 3, 4, - 8) and is parallel to the vector b = 3i^ + 5j^ + 6k^

Let M be the foot of the perpendicular from P(- 2, 4, - 5) on the given line.

We, have

 AP = 1 + 0 + 9 = 10

Clearly, AM = Projection of AP on b

 AM = AP . bb            = - i^ - 3k^3i^ + 5j^ + 6k^3i^ + 5j^ + 6k^            = - 3 - 189 + 25 + 36 = - 2170 = 2170 PM = AP2 - AM2           = 10 - 44170 = 25970           = 3710


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313.

The equation of straight line passing through the point (a, b, c) and parallel to Z-axis, is

  • x - a1 = y - b1 = z - c0

  • x - a0 = y - b1 = z - c1

  • x - a1 = y - b0 = z - c0

  • x - a0 = y - b0 = z - c1


314.

If the equation of the locus of a point equidistant from the points (a1, b1) and (a2, b2) is (a1 - a2)r + (b1 - b2)y + c = 0, then the value of 'c' is

  • 12a22 + b22 - a12 - b12

  • a12 - a22 + b12 - b22

  • 12a12 + a22 + b12 + b22

  • a12 + b12 - a22 - b22


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315.

A tetrahedron has vertices at 0(0, 0, 0), A(1, 2, 1), B(2, 1, 3) and C(- 1, 1, 2). Then, the angle between the faces OAB and ABC will be

  • cos-11935

  • cos-11731

  • 30°

  • 90°


316.

Distance between parallel planes 2x - 2y + z + 3 = 0 and 4x - 4y + 2z + 5 = 0, is

  • 12

  • 13

  • 14

  • 16


317.

Given two vectors i^ - j^ and i^ + 2j^, the unit vector coplanar with the two vectors and perpendicular to first, is

  • 12i^ + j^

  • 152i^ + j^

  • ± 12i^ + j^

  • None of these


318.

If a and b are unit vectors and θ is the angle between them, then the value of cosθ2 is

  • 12a + b

  • 12a - b

  • a - ba + b

  • a + ba - b


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319.

If aa21 + a3bb21 + b3cc21 + c3 and vectors (1, a, a2), (1, b, b2) and (1, c, c2) are non-coplanar, then the product abc equals

  • 2

  • - 1

  • 1

  • 0


320.

If the length of perpendicular drawn from origin on a plane is 7 unit and its direction ratios are - 3, 2 and 6, then that plane is

  • - 3x + 2y + 6z - 7 = 0

  • - 3x + 2y + 6z - 49 = 0

  • 3x - 2y + 6z + 7 = 0

  • - 3x + 2y - 6z - 49 = 0


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