Question

# For given vectors, and , find the unit vector in the direction of the vector

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Solution

## The given vectors are a → =2 i ^ − j ^ +2 k ^ and b → =− i ^ + j ^ − k ^ . Sum of vector a → and b → is, ( a → + b → )=( 2−1 ) i ^ +( −1+1 ) j ^ +( 2−1 ) k ^ =1 i ^ +0 j ^ +1 k ^ = i ^ + k ^ Consider, c → = i ^ + k ^ . Magnitude of vector c → is, | c → |= 1 2 + 0 2 + 1 2 = 2 The unit vector in direction of c → is, c ^ = c → | c → | = i ^ + k ^ 2 = 1 2 i ^ + 1 2 k ^ Thus, the unit vector in direction of sum of vector a → and b → is 1 2 i ^ + 1 2 j ^ .

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