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

Open in App

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 ^ .

Suggest Corrections

Similar questions

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

\to a = 2 ˆ i - ˆ j + 2 ˆ k

\to b = - ˆ i + ˆ j - ˆ k

\to a + \to b

\to a = 2^i -^j + 2^k

\to b = -^i +^j -^k

\to a + \to b

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

\to a = 2 ˆ i - ˆ j + 2 ˆ k

b = - ˆ i + ˆ j - ˆ k

\to a + \to b

Join BYJU'S Learning Program