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Question

The component of vector 2^i−3^j+2^k perpendicualr to ^i+^j+^k is:

A
53(^i2^j+^k)
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B
13(^i+^j2^k)
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C
(7^i10^j+7^k)3
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D
(5^i8^j+5^k)3
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Solution

The correct option is A 53(^i−2^j+^k)Let, two vectors be →a=2^i−3^j+2^k, →b=^i+^j+^k We know the component of vector of →a perpendicular to →b can be given by: →c=→a−⎛⎜⎝→a.→b|→b|2⎞⎟⎠→b⋯(i) Now, →a.→b=(2^i−3^j+2^k).(^i+^j+^k) ⇒→a.→b=2−3+2=1 Now putting all these values in equation (i), we will get: →c=(2^i−3^j+2^k)−1(√3)2×(^i+^j+^k) =(2^i−3^j+2^k)−13×(^i+^j+^k) =(2−13)^i+(−3−13)^j+(2−13)^k =53^i−103^j+53^k ⇒→c=53(^i−2^j+^k)

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