A force F =( hat i +2 hat j +3 hat k ) N acts at a point (4 hat i +3 hat j - hat k ) m ⋅ Then the magnitude of torque about the point ( hat i +2 hat j + hat k ) m will be √ x N - m . The value of x is .

Question

A force F =( hat i +2 hat j +3 hat k ) N acts at a point (4 hat i +3 hat j - hat k ) m ⋅ Then the magnitude of torque about the point ( hat i +2 hat j + hat k ) m will be √ x N - m . The value of x is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

vecτ=( vec r 2- vec r 1) × vec F =[(4 hat i +3 hat j - hat k )-( hat i +2 hat j + hat k )] × vec F =(3 hat i + hat j -2 hat k ) ×( hat i +2 hat j +3 hat k ) τ=| hati& hatj& hatk 3&1&-2 1&2&3| =7 hati-11 hatj+5 hatk | vecτ|=√195

Q. A force F=(i^+2j^​+3k^)N acts at a point (4i^+3j^​−k^)m⋅ Then the magnitude of torque about the point (i^+2j^​+k^)m will be x​N−m. The value of x is ____.

τ=(r2​−r1​)×F =[(4i^+3j^​−k^)−(i^+2j^​+k^)]×F =(3i^+j^​−2k^)×(i^+2j^​+3k^) τ=∣∣​i^31​j^​12​k^−23​∣∣​ =7i^−11j^​+5k^ ∣τ∣=195​

Q. A force $F = (\hat{i} + 2 \hat{j} + 3 \hat{k}) N$ acts at a point $(4 \hat{i} + 3 \hat{j} - \hat{k}) m \cdot$ Then the magnitude of torque about the point $(\hat{i} + 2 \hat{j} + \hat{k}) m$ will be $x N - m .$ The value of $x$ is ____.