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The acute angle between the line ...

The acute angle between the line
` bar r = ( hati + 2 hatj + hatk ) + lamda (hati + hatj +hatk)`
and the plane `bar r ( 2hati - hatj +hatk)=5`

A

`cos^(-1) ""((sqrt(2))/(3))`

B

`sin ^(-1) ((sqrt(2))/(3))`

C

`tan ^(-1) ""((sqrt(2))/(3))`

D

`sin ^(-1) ""((sqrt(2))/(sqrt(3)))`

Text Solution

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The correct Answer is:
B
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The angle between the line vecr = ( 5 hati - hatj - 4 hatk ) + lamda ( 2 hati - hatj + hatk) and the plane vec r.( 3 hati - 4 hatj - hatk) + 5=0 is

Find the angle between the line barr = (hati + 2hatj + hatk) + lambda(hati +hatj + hatk) and the plane barr*(2hati - hatj + hatk) = 5 .

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Find the angle between the pair of lines bar r = ( 3 hati + 2 hatj - 4hatk ) + lamda ( hati + 2hatj + 2hatk ) and bar r = ( 5hati - 2 hatk ) + mu ( 3hati + 2 hatj + 6 hatk )

The angle between the lines bar(r) = (2hati - 5hatj + hatk) + lamda(3hati + 2hatj + 6 hatk ) "and" bar(r) = (7hati - 6hatk) + mu(hati + 2hatj + 2hatk) is

(i) Find the distance of the point (-1,-5,-10) from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk ) + lambda (3 hati + 4 hatj + 12 hatk) and the plane vec(r).(hati - hatj + hatk) = 5. (ii) Find the distance of the point with position vector - hati - 5 hatj - 10 hatk from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk ) + lambda (3 hati + 4 hatj + 12 hatk ) and the plane vec(r). (hati - hatj + hatk)= 5. (iii) Find the distance of the point (2,12, 5) from the point of intersection of the line . vec(r) = 2 hati - 4 hatj + 2 hatk + lambda (3 hati + 4 hatj + 12 hatk ) and the plane vec(r). (hati - 2 hatj + hatk ) = 0.

The shortest distance between the lines r = ( - hati - hatj - hatk ) + lamda ( 7 hati - 6 hatj + hatk ) and r = ( 3 hati + 5 hatj + 7 hatk ) + mu ( hati - 2 hatj + hatk )

Find the shortest distance betwee the lines : vec(r) = (hati + 2 hatj + hatk ) + lambda ( hati - hatj + hatk) and vec(r) = 2 hati - hatj - hakt + mu (2 hati + hatj + 2 hatk) .

Find the distance of the point with position vector - hati - 5 hatj - 10 hatk from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk) + lambda ( 3 hati + 4 hatj + 12 hatk) with the plane vec(r). (hati - hatj + hatk) = 5 .

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