Question

If vectors  \(\rm \vec a = \vec b\) then a₃ is ?

Where \(\rm \vec a = 5\hat i - 3\hat j +a_3\hat k\) and \(\rm \vec b =\rm \vec 5\hat i - 3\hat j -2\hat k\) 

1. - 2
2. -1
3. 2
4. 1

Answer 1

Correct Answer - Option 1 : - 2

Concept:

Equal Vectors
Two or more vectors are said to be equal when their magnitude is equal and also their direction is the same.

Calculation:

Given:  \(\rm \vec a = 5\hat i - 3\hat j +a_3\hat k\) and  \(\rm \vec b =\rm \vec 5\hat i - 3\hat j -2\hat k\) 

\(\rm \vec a = \vec b\)

 \(\rm 5\hat i - 3\hat j +a_3\hat k =\rm \vec 5\hat i - 3\hat j -2\hat k\)

∴ a3 = - 2