Find the angle between the following pai...

Find the angle between the following pair of lines: A lines with direction ratios 2,2,1 A line joning (3,1,4)to (7,2,12)

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:

A

Given DR's 2,2,1
The DR's of the line joining (2,1,4) to (7,2,12) are 7,-3,2-1,12-44,1,8
`costheta=(4xx2+1xx2+8xx1)/(sqrt(4^2+1^2+8^2)sqrt(2^2+2^2+1^2))`
`=(18)/(sqrt(81)sqrt(9))=(18)/(9xx3)`
`costheta=2/3rArrtheta=cos^(-1)(2/3)`

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