For given vectors →a=2ˆi−ˆj+2ˆk and b=−ˆi+ˆj−ˆk, then a unit vector in the direction of the vector →a+→b is
A
ˆi+ˆj−2ˆk
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B
1√2ˆi+1√2ˆk
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C
√2ˆi+√2ˆk
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D
None
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Solution
The correct option is D1√2ˆi+1√2ˆk Now →a=2ˆi−ˆj+2ˆk and →b=−ˆi+ˆj−ˆk Thus →a+→b=(2ˆi−ˆj+2ˆk)+(ˆi+ˆj−ˆk)=ˆi+ˆk Now |→a+→b|=√12+12=√2 Hence, unit vector along →a=→a+→b|→a+→b| =1√2ˆi+1√2ˆk