If A⃗ = 4î − 2ĵ + 6k̂ and B⃗ = î − 2ĵ − 3k̂, the angle of A⃗+B⃗ with the positive x-axis is cos⁻¹(P/√50). Find P.
Physics · Mixed Chapter
JEE Main Practice

Question

If A⃗ = 4î − 2ĵ + 6k̂ and B⃗ = î − 2ĵ − 3k̂, the angle of A⃗+B⃗ with the positive x-axis is cos⁻¹(P/√50). Find P.

G1 Physics · Accepted Answer

Step 1: Add components: A⃗+B⃗ = 5î − 4ĵ + 3k̂. Step 2: Magnitude = √(25+16+9) = √50. Step 3: Direction cosine with the x-axis is 5/√50. Thus P = 5.