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Question

write the number of vectors of unit length perpendicular to both the vectors a=2^i+^j+2^k and b=^j+^k.

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Solution

a=2^i+^j+2^k
b=^j+^k

a×b=∣ ∣ ∣^i^j^k212011∣ ∣ ∣

=^i(12)^j(20)+^k(20)

=^i2^j+2^k22+22+1

=^i2^j+2^k9

=^i2^j+2^k3

(a×b)=(^i2^j+2^k)3

=^i+2^j2^k3

1959543_1493128_ans_6a54d135072c407e99e504cfaf9d6985.PNG

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