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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 )=( 21 ) i ^ +( 1+1 ) j ^ +( 21 ) 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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