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Question

Let a=2^i+2^j+^k and b be another vector such that ab=14 and a×b=3^i+^j8^k then the vector b is equal to

A
5^i+^j+2^k
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B
5^i^j2^k
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C
5^i+^j2^k
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D
3^i+^j+4^k
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Solution

The correct option is A 5^i+^j+2^k
Let b=x^i+y^j+z^k
Given ab=142x+2y+z=14(1)
a×b=3^i+^j8^k
a×b=∣ ∣ ∣^i^j^k221xyz∣ ∣ ∣=3^i+^j8^k
2zy=3y=2z3(2)
(2zx)=1x=2z+1(3)
Substitute equation (2),(3) in equation (1), we get
z=2, y=1, x=5
b=5^i+^j+2^k

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