If A⃗=(2î+3ĵ-k̂) m and B⃗=(î+2ĵ+2k̂) m. The magnitude of component of vector A⃗ along vector B⃗ will be ____________ m.

Solution

Physics sir · 4 steps

Component of A along B means dot A with the unit vector of B: divide the dot product by |B|.

1. Set up. The component of A⃗ along B⃗ is A⃗ · B. Since B = B⃗/|B⃗|, you divide the dot product by the length of B⃗.

   A_B = (A⃗ · B⃗)/|B⃗|

2. Dot product. Multiply matching components and add: A⃗ · B⃗ = (2)(1) + (3)(2) + (-1)(2) = 2 + 6 - 2 = 6 m².
3. Length of B. |B⃗| = √(1² + 2² + 2²) = √9 = 3 m.
4. So. A_B = 6/3 = 2 m, so the answer is 2.

The common slip: 1.6. Dividing the dot product by |A⃗| = √14 instead of |B⃗| = 3 gives 6/√14 ≈ 1.6, not 2.

The idea to keep. To find the component of one vector along another, divide the dot product by the length of the vector you are projecting onto. Keep every minus sign when you take the dot product.

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