If the force represented by i + j + k is acting through the point 5 i +4 j -3 k, then its moment about the point (1,2,2) is

Question

If the force represented by i + j + k is acting through the point 5 i +4 j -3 k, then its moment about the point (1,2,2) is (A) 14 i -8 j +12 k (B) -14 i -8 j -12 k (C) 7 i +9 j +2 k (D) 7 i -9 j +2 k

Tardigrade Admin · Accepted Answer

We have, F = i + j + k Let P(5,4,-3) and O(1,2,2) be given points. Then, O P=4 i +2 j -5 k Now, moment of F about O =r × F| beginarrayccc i j k 4 2 -5 1 1 1 endarray|=(2+5) i -(4+5) j +(4-2) k

Q. If the force represented by $i + j + k$ is acting through the point $5 i + 4 j - 3 k$ , then its moment about the point $(1, 2, 2)$ is

$14 i - 8 j + 12 k$

$- 14 i - 8 j - 12 k$

$7 i + 9 j + 2 k$

$7 i - 9 j + 2 k$

We have, $F = i + j + k$ Let $P (5, 4, - 3)$ and $O (1, 2, 2)$ be given points. Then, $OP = 4 i + 2 j - 5 k$
Now, moment of $F$ about $O$ $= r \times F ∣ ∣ i 41 j 21 k - 5 1 ∣ ∣ = (2 + 5) i - (4 + 5) j + (4 - 2) k$

Q. If the force represented by i+j+k is acting through the point 5i+4j−3k, then its moment about the point (1,2,2) is

14i−8j+12k

−14i−8j−12k

7i+9j+2k

7i−9j+2k