Find the vector of magnitude 10 perpendicular to both 2î-ĵ+3k̂ and î+2ĵ-k̂, with positive k-component.
Options

Question

Find the vector of magnitude 10 perpendicular to both 2î-ĵ+3k̂ and î+2ĵ-k̂, with positive k-component.

G1 Physics · Accepted Answer

The cross product (2,−1,3)×(1,2,−1)=−5î+5ĵ+5k=5(−î+ĵ+k̂), whose magnitude is 5√3. The unit normal with positive k-component is (−î+ĵ+k̂)/√3. Multiplying by 10 gives the answer.