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Question

A unit vector parallel to the intersection of the planes r(^i^j+^k)=5 and r(2^i+^j3^k)=4 can be

A
2^i+5^j+3^k38
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B
2^i5^j+3^k38
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C
2^i5^j3^k38
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D
2^i+5^j3^k38
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Solution

The correct options are
A 2^i+5^j+3^k38
D 2^i5^j3^k38
Vector parallel to intersection of planes

p=∣ ∣ ∣^i^j^k111213∣ ∣ ∣

=^i(31)^j(32)+^k(1+2)

=2^i+5^j+3^k

|p|=22+52+32=38

unit vector parallel to intersection of planes

=±(2^i+5^j+3^k)22+52+32

=±(2^i+5^j+3^k)38

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