Find the unit vector in the direction of sum of vectors vector a = 2i - j + k and vector b = 2j + k.

Question

Find the unit vector in the direction of sum of vectors \(\vec a = 2 \hat i - \hat j + \hat k \) and \(\vec b = 2 \hat j + \hat k.\)

Answer 1

We have,

\(\vec a = 2 \hat i - \hat j + \hat k \)

\(\vec b = 2 \hat j + \hat k.\)

Since, unit vector is needed to be found in the direction of the sum of vectors \(\vec a\) and \(\vec b\).

So, add vectors \(\vec a\) and \(\vec b\).

Let,

We know that, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

To find a unit vector with the same direction as a given vector, we divide by the magnitude of the vector.

For finding unit vector, we have the formula:

Substitute the value of \(\vec c\).