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A unit vector parallel to the intersection of the planes ` vec r. \ ( hat i- hat j+ hat k)=5 \ a n d \ vec r. \ (2 hat i+ hat j-3 hat k)=4` a. `(2 hat i+5 hat j-3 hat k)/(sqrt(38))` b. `(-2 hat i+5 hat j-3 hat k)/(sqrt(38))` c. `(2 hat i+5 hat j-3 hat k)/(sqrt(38))` d. `(-2 hat i-5 hat j-3 hat k)/(sqrt(38))`

A

`(2hati+5hatj-3hatk)/(sqrt38)`

B

`(2hati-5hatj+3hatk)/(sqrt38)`

C

`(-2hati-5hatj-3hatk)/(sqrt38)`

D

`(-2hati+5hatj-3hatk)/(sqrt38)`

Text Solution

Verified by Experts

The correct Answer is:
C
`hata=pm(vecn_(1)xxvecc_(2))/(|vecn_(1)xxvec n_(2)|)=pm(2hati+5hatj+3hatk)/(sqrt38)`
(where `vecn_(1)andvecn_(2)` are normal to the planes)
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CENGAGE PUBLICATION-THREE-DIMENSIONAL GEOMETRY -SINGLE CORRECT ANSWER TYPE
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