Question

A vector \(\overset{⃗}{A}\) when added to the sum of the vectors \((\hat{i}-2\hat{j}+2\hat{k})\) and \((-2\hat{i}+\hat{j}-\hat{k})\) gives a unit vector along Y axis. The magnitude of vector \(\overset{⃗}{A}\) is

• A. \(\sqrt{3}\)
• B. \(\sqrt{6}\)
• C. \(\sqrt{8}\)
• D. \(\sqrt{10}\)

Hint:

Subtract the sum of the two vectors from j.

Answer 1

The Correct Option is B

Step 1: Component by component:
Let $\vec A=(a_1,a_2,a_3)$. The total $\vec A+\vec S$ must equal $(0,1,0)$.

Step 2: Solve:
$a_1-1=0\Rightarrow a_1=1$. $a_2-1=1\Rightarrow a_2=2$. $a_3+1=0\Rightarrow a_3=-1$.

Step 3: Length:
$\sqrt{1^2+2^2+(-1)^2}=\sqrt6$. Option (B).

Final Answer:
Components (1, 2, -1) give length sqrt 6. \[ \boxed{B} \]