Find a vector in the direction of vector a = 2 i - j + 2k, which has magnitude of 6 units.

Question

Find a vector in the direction of  \(\vec a=2\hat i-\hat j+2\hat k\)  which has magnitude of 6 units.

Answer 1

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

The unit vector of any vector  \(\vec a=a_1\hat i+a_2\hat j+a_3\hat k\) can be written as

Let the required vector be \(\vec d\).

Any vector (\(\vec p\)) with magnitude m and unit vector  \(\hat a\) can be written as  \(\vec p=m\times\vec a\).

Since the magnitude of  \(\vec d\) is 6 and it’s unit vector is \(\vec a\), we get