The moment about the point hat i +2 hat j +3 hat k of a force represented by hat i + hat j + hat k acting through the point 2 i +3 j + k is

Question

The moment about the point hat i +2 hat j +3 hat k of a force represented by hat i + hat j + hat k acting through the point 2 i +3 j + k is (A) 3 hati+3 hatj (B) 3 hat i + hat j  (C) - hat i + hat j  (D) 3 hati-3 hatj

Tardigrade Admin · Accepted Answer

Here, r=(2 i+3 j+k)-(i+2 j+3 k) ⇒ r = i + hat j -2 hat k and F = i + hat j + hat k Then, the required moment is given by r × F=(i+ hatj-2 hatk) ×(i+ hatj+ hatk)=| hati hatj hatk 1 1 -2 1 1 1|=3 hati-3 hatj ∴ Moment about given point =3 hat i -3 hat j

Q. The moment about the point $\hat{i} + 2 \hat{j} + 3 \hat{k}$ of a force represented by $\hat{i} + \hat{j} + \hat{k}$ acting through the point $2 i + 3 j +$ $k$ is

$3 \hat{i} + 3 \hat{j}$

$3 \hat{i} + \hat{j}$

$- \hat{i} + \hat{j}$

$3 \hat{i} - 3 \hat{j}$

Q. The moment about the point i^+2j^​+3k^ of a force represented by i^+j^​+k^ acting through the point 2i+3j+ k is

3i^+3j^​

3i^+j^​

−i^+j^​

3i^−3j^​

Here, r=(2i+3j+k)−(i+2j+3k) ⇒r=i+j^​−2k^ and F=i+j^​+k^ Then, the required moment is given by r×F=(i+j^​−2k^)×(i+j^​+k^)=∣∣​<br/><br/>i^11​j^​11​k^−21​∣∣​=3i^−3j^​ ∴ Moment about given point =3i^−3j^​

Q. The moment about the point $\hat{i} + 2 \hat{j} + 3 \hat{k}$ of a force represented by $\hat{i} + \hat{j} + \hat{k}$ acting through the point $2 i + 3 j +$ $k$ is

$3 \hat{i} + 3 \hat{j}$

$3 \hat{i} + \hat{j}$

$- \hat{i} + \hat{j}$

$3 \hat{i} - 3 \hat{j}$