When vector \vecA=2 \hati+3 \hatj+2 \hatk is subtracted from vector \overrightarrowB , it gives a vector equal to 2 \hatj . Then the magnitude of vector \overrightarrowB will be :

Vector Algebra PYQ — JEE Main 2023 · 11 Apr · Shift 2 · Q57 with Solution

View written solutionFree

Correct answer: B

Interpret the statement

“Vector $\vec A$ is subtracted from vector $\vec B$ and it gives $2\hat j$ ” means $\vec B - \vec A = 2\hat j$
Write the given vector

$\vec A = 2\hat i + 3\hat j + 2\hat k$

Also, $2\hat j = 0\hat i + 2\hat j + 0\hat k$
Find $\vec B$

From $\vec B - \vec A = 2\hat j$ we get $\vec B = \vec A + 2\hat j$

Substitute $\vec A$ : $\vec B = (2\hat i + 3\hat j + 2\hat k) + 2\hat j$ $\vec B = 2\hat i + 5\hat j + 2\hat k$
Calculate the magnitude of $\vec B$

$|\vec B| = \sqrt{2^2 + 5^2 + 2^2}$ $|\vec B| = \sqrt{4+25+4} = \sqrt{33}$
Check options
- A: $3$
- B: $\sqrt{33}$ ✅
- C: $\sqrt6$
- D: $\sqrt5$

Therefore, the correct option is B.