When vector A⃗=2î+3ĵ+2k̂ is subtracted from vector B⃗, it gives a vector equal to 2ĵ. Then the magnitude of vector B⃗ will be :

Solution

Physics sir · 3 steps

Read "A subtracted from B" as B minus A, then move A across to get B on its own.

1. Set up the equation. "A subtracted from B" means B⃗ - A⃗, so B⃗ - A⃗ = 2ĵ. Adding A⃗ to both sides gives B⃗ = A⃗ + 2ĵ.
2. Add component-wise. Only the ĵ component changes: B⃗ = 2î + (3+2)ĵ + 2k̂ = 2î + 5ĵ + 2k̂.

   |B⃗| = √(2² + 5² + 2²) = √(4 + 25 + 4) = √33

3. So. The magnitude of B⃗ is √33, which is option (b).

The idea to keep. "X subtracted from Y" always means Y minus X. Get the order right, solve for the unknown vector component by component, and only then take its magnitude.

Answer from the NTA final answer key. Solution by PrepWiser.