A unit vector perpendicular to the plane of a = 2i

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 Multiple Choice QuestionsMultiple Choice Questions

341.

The angle between the straight lines x + 12 = y - 25 = z + 34 and x - 11 = y + 22 = z - 3- 3 is

  • 45°

  • 30°

  • 60°

  • 90°


342.

The acute angle between the planes 2x - y + z = 6 and x + y + 2z = 3 is

  • 45°

  • 60°

  • 30°

  • 90°


343.

The ratio in which the line joining the points (2, 4, 5) and (3, 5, - 4) is divided by the YZ-plane, is

  • 2 : 3

  • 3 : 2

  • - 2 : 3

  • 4 : - 3


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344.

A unit vector perpendicular to the plane of a = 2i^ - 6j^ - 3k^b = 4i^ + 3j^ - k^, is

  • 4i^ + 3j^ - k^26

  • 2i^ - 6j^ - 6k^7

  • 3i^ - 2j^ + 6k^7

  • 2i^ - 3j^ - 6k^7


C.

3i^ - 2j^ + 6k^7

Given, a = 2i^ - 6j^ - 3k^ and b = 4i^ + 3j^ - k^ a × b = i^j^k^2- 6- 343- 1= i^6 + 9 - j^- 2 + 12 + k^6 + 24= 15i^ - 10j^ + 30k^and a × b = 225 + 100 + 900                    = 1225 = 35Hence, unit vector perpendicular to a and b                   = a × ba × b                   = 15i^ - 10j^ + 30k^35                   = 3i^ - 2j^ + 6k^7


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345.

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

  • 5/2

  • 3/5

  • 7/3

  • None of these


346.

The ratio rn which the XY- plane meets the line joining the points (- 3, 4, - 8)and (5, - 6, 4 ) is

  • 2 : 3

  • 2 : 1

  • 4 : 5

  • None of these


347.

If a, b c are coplanar vectors, then which of the following is not correct ?

  • a . b × c = 0

  • a × b × c = 0

  • [a + b, b + c, c + a] = 0

  • a = pb + qc


348.

Find the equation of plane through the line x - 22 = y - 33 = z - 45 and parallel to X-axis.

  • 2x + 3y + 5z = 1

  • 2x - 3z - 3 = 0

  • 5y - 3z - 3 = 0

  • 3y + 4z = 0


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349.

The value of 'λ', so that the vectors i^ - 3j^ + k^2i^ + λj^ + k^ and 3i^ + j^ - 2k^ are coplanar, will be

  • 0

  • 2

  • - 12

  • - 4


350.

The line passing through the point (- 1, 2 3) and perpendicular to the plane x - 2y + 3z+ 5 = 0 will be

  • x + 11 = y - 23 = z - 35

  • x + 11 = y - 23 = z + 33

  • x + 11 = y - 23 = z - 32

  • x + 11 = y - 2- 2 = z - 33


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