If P ⃗ \vec{P} P = 3î + √3ĵ + 2k̂ and Q ⃗ \vec{Q} Q = 4î + √3ĵ + 2.5k̂, then the unit vector in the direction of P ⃗ \vec{P} P × Q ⃗ \vec{Q} Q is (1/x)(√3î + ĵ - 2√3k̂). The value of x is:
Physics · Mathematical tools and vector
JEE Mains 25 January 2023 Morning Shift

Question

If P ⃗ \vec{P} P = 3î + √3ĵ + 2k̂ and Q ⃗ \vec{Q} Q = 4î + √3ĵ + 2.5k̂, then the unit vector in the direction of P ⃗ \vec{P} P × Q ⃗ \vec{Q} Q is (1/x)(√3î + ĵ - 2√3k̂). The value of x is:

Physics · Mathematical tools and vector

JEE Mains 25 January 2023 Morning Shift

G1 Physics · Accepted Answer

P⃗ × Q⃗ = (√3/2)î + (1/2)ĵ - √3k̂. Its magnitude is 2. Therefore the unit vector is (√ 3 4 \frac{3}{4} 4 3 ​ )î + (1/4)ĵ - (√3/2)k̂ = (1/4)(√3î + ĵ - 2√3k̂). Hence x = 4.

If P ⃗ \vec{P} P = 3î + √3ĵ + 2k̂ and Q ⃗ \vec{Q} Q ​ = 4î + √3ĵ + 2.5k̂, then the unit vector in the direction of P ⃗ \vec{P} P × Q ⃗ \vec{Q} Q ​ is (1/x)(√3î + ĵ - 2√3k̂). The value of x is:

If P ⃗ \vec{P} P = 3î + √3ĵ + 2k̂ and Q ⃗ \vec{Q} Q = 4î + √3ĵ + 2.5k̂, then the unit vector in the direction of P ⃗ \vec{P} P × Q ⃗ \vec{Q} Q is (1/x)(√3î + ĵ - 2√3k̂). The value of x is: