Question

If \( \overrightarrow a = \hat i + 2\hat j - 3\hat k\), and \( \overrightarrow b = 2\hat i + 4\hat j - 5\hat k\). Find a unit vector parallel to \( \overrightarrow a + \overrightarrow b\).

Answer 1

Answer:

(3/√109) i  +  (6/√109) j  -  (8/√109) k

Hope this helps you.

Step-by-step explanation:

Let

c = a + b = ( i + 2j - 3k ) + ( 2i + 4j - 5k ) = 3i + 6j - 8k

This is a vector parallel to a+b  (it is a+b!)

To get a unit vector parallel to this, we just divide by the magnitude of c.

|c| = √( 3² + 6² + 8² ) = √( 9 + 36 + 64 ) = √109.

So a unit vector parallel to a+b is

c / |c|

= ( 3i + 6j - 8k ) / √109

= (3/√109) i  +  (6/√109) j  -  (8/√109) k