The unit vector in the direction of the sum of vectors \(\vec{a}=2\hat{\imath}+2\hat{\jmath}-5\hat{k}\) and \(\vec{a}=2\hat{\imath}+\hat{\jmath}+3\hat{k}\) is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{4}{\sqrt{29}}\hat{\imath}+\frac{3}{\sqrt{29}}\hat{\jmath}-\frac{2}{\sqrt{29}}\hat{k}\)
Adding the two given vectors component by component:
\((2+2)\hat{\imath} + (2+1)\hat{\jmath} + (-5+3)\hat{k} = 4\hat{\imath}+3\hat{\jmath}-2\hat{k}\)
Its magnitude:
\(\sqrt{16+9+4} = \sqrt{29}\)
The unit vector is the vector divided by its magnitude:
\( \displaystyle \frac{4}{\sqrt{29}}\hat{\imath}+\frac{3}{\sqrt{29}}\hat{\jmath}-\frac{2}{\sqrt{29}}\hat{k} \)
NCERT (2026-27 edition):
Components of a Vector
