Force F⃗=(2î−3ĵ+4k̂) acts at position r⃗=(Pî+Qĵ+3k̂). Torque about origin is τ⃗=(17î−6ĵ−13k̂). Find P+Q.
Physics · Mixed Chapter
JEE Main Practice

Question

Force F⃗=(2î−3ĵ+4k̂) acts at position r⃗=(Pî+Qĵ+3k̂). Torque about origin is τ⃗=(17î−6ĵ−13k̂). Find P+Q.

G1 Physics · Accepted Answer

Step 1: Compute τ⃗=r⃗×F⃗=(4Q+9)î+(6−4P)ĵ+(−3P−2Q)k̂. Step 2: Equate î components: 4Q+9=17 ⇒Q=2. Equate ĵ components: 6−4P=−6 ⇒P=3. Step 3: k̂ component check: −3×3−2×2=−13, which matches. Step 4: P+Q=3+2=5; the PDF prints 7, which is inconsistent with its own torque vector.