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Question

If a=^i+2^j+^k, b=2^i+^j^k, then component of a perpendicular to b is

A
^5i2+^2i3+^k2
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B
^5i3+2^i+^k3
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C
(5^i+2^i+^k)3
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D
1.5^j+1.5^k
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Solution

The correct option is C 1.5^j+1.5^k
The component of ¯¯¯a along ¯¯b is (¯¯¯a.¯¯b)¯¯b|¯¯b|2
So, the component perpendicular to ¯¯b will be ¯¯¯a(¯¯¯a.¯¯b)¯¯b|¯¯b|2
Thus, the component =(¯i+2¯j+¯¯¯k)36(2¯i+¯j¯¯¯k)=1.5¯j+1.5¯¯¯k

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