For given vectors, →a=2^i−^j+2^k and →b=−^i+^j−^k, find the unit vector in the direction of the vector →a+→b
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Solution
The given vectors are →a=2^i−^j+2^k and →b=−^i+^j−^k. ∴→a+→b=(2−1)^i+(−1+1)^j+(2−1)^k=1^i+0^j+1^k=^i+^k ∣∣→a+→b∣∣=√12+12=√2 Hence, the unit vector in the direction of (→a+→b) is (→a+→b)|→a+→b|=^i+^k√2=1√2^i+1√2^k.