A vector has magnitude same as that of A⃗=3î+4ĵ and is parallel to B⃗=4î+3ĵ. The x and y components of this vector in first quadrant are x and 3 respectively where x= _________.

Solution

Physics sir · 3 steps

Take the unit vector along B, then stretch it to the length of A.

1. Magnitude needed. The new vector must have the same length as A⃗: |A⃗| = √(3² + 4²) = 5.
2. Direction needed. It must point along B⃗. Here |B⃗| = √(4² + 3²) = 5, so the unit vector along B⃗ is B = (4î + 3ĵ)/5.

   C⃗ = |A⃗| B = 5 × (4î + 3ĵ)/5 = 4î + 3ĵ

3. So. Both components are positive, so the vector lies in the first quadrant. Its y component is 3, which matches the question, and its x component is 4.

The idea to keep. Any vector with a given length and direction is (length) times (unit vector in that direction). Find the magnitude and the unit vector separately, then multiply.

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