The plane passing through the points (1, 2, 1), (2, 1, 2) and par

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 Multiple Choice QuestionsMultiple Choice Questions

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431.

The plane passing through the points (1, 2, 1), (2, 1, 2) and parallel to the line, 2x = 3y, z = 1 also passes through the point :

  • (2, 0, - 1)

  • (0, 6, - 2)

  • (0,  - 6, 2)

  • (- 2, 0 , 1)


D.

(- 2, 0 , 1)

Plane passes through 2, 1, 2 isax - 2 + by - 1 +z - 2 = 0    iit also passes through (1, 2, 1)so, a1 - 2 +b2 - 1 +c1 - 2 = 0 a +b - c = 0 a - b + c = 0   ... iiline 2x = 3y and z = 1, is parallel to plane ix3 = y2 = z - 10, is parallel to plane iso, 3a + 2b + c 0 = 0 3a +2b = 0    ... iiifrom cramers rulea - 1 × 0 - 1 × 2 =  - b1 × 0 - 1 × 3 = c1 × 2 -  - 1 × 3a - 2 = b3 = c5so, plane is - 2x - 2 + 3y - 1 +5z - 2 = 0 2x + 3y + 5z +4 - 3 - 10 = 0 2x =3y +5z - 9 = 0here we get, - 2, 0 , 1 satisfies the plane


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432.

A plane passing through the point (3, 1, 1) contains two lines whose direction ratios are 1, – 2, 2 and 2, 3, – 1 respectively. If this plane also passes through the point(α,–3, 5), then α is equal to

  • 5

  • 10

  •  - 5

  •  - 10


433.

Let the latus rectum of the parabola y= 4x be the common chord to the circles C1 and C2 each of them having radius 25. Then, the distance between the centres of the circles C1 and C2 is :

  • 12

  • 8

  • 85

  • 45


 Multiple Choice QuestionsShort Answer Type

434.

Let a plane P contain two linesr = i^ + λi^ + j^, λ  R andr = - j^ + μj^ - k^, μ  RIf Qα, β, γ is the foot of the perpendicular drawn from the point equals...


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 Multiple Choice QuestionsMultiple Choice Questions

435.

The shortest distance between the lines x - 10 = y + 1 - 1 = z1 and x + y + z + 1 = 0, 2x - y + z + 3 = 0 is

  • 12

  • 1

  • 13

  • 12


 Multiple Choice QuestionsShort Answer Type

436.

The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45°. After waling a distance of 80 meters towards the top, up a slope inclined at angle of 30° to the horizontal plane the angle of elevation of the top of the hill becomes 75°. Then the height of the hill (in meters) is _____.


 Multiple Choice QuestionsMultiple Choice Questions

437.

A plane P meets the coordinate axes at A, B and C respectively. The centroid of ABC is given to be (1, 1, 2). Then the equation of the line through this centroid and perpendicular to the plane P is:

  • x - 12 = y - 11 = z - 21

  • x - 11 = y - 12 = z - 22

  • x - 11 = y - 11 = z - 22

  • x - 12 = y - 12 = z - 21


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