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The angle between i and line of the inte...

The angle between `i` and line of the intersection of the plane ` vec r . ( hat i+2 hat j+3 hat k)=0` and `vec r . (3 hat i+3 hat j+ hat k)=0` is a. `cos^(-1)(1/3)` b. `cos^(-1)(1/(sqrt(3)))` c. `cos^(-1)(2/(sqrt(3)))` d. none of these

A

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

B

`cos^(-1)((1)/(sqrt3))`

C

`cos^(-1)((2)/(sqrt3))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
d
Line of intersection of `vecr.(hati+2hatj+3hatk)=0andvecr.(3hati+3hatj+hatk)=0` will be parellel to `(hati+hatj+hatk)xx(hati+2hatj+3hatk),i.e.,7hati-8hatj+3hatk.`
If the required angle is `theta`, then
`costheta=(7)/(sqrt(49+64+9))=(7)/(sqrt122)`
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CENGAGE PUBLICATION-THREE-DIMENSIONAL GEOMETRY -SINGLE CORRECT ANSWER TYPE
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