A force $\to F = 4^i + 3^j + 4^K$ is applied on an intersection point of $x = 2$ plane and $x - axis$ . The magnitude of torque of this force about a point $(2, 3, 4)$ is (Round off to the Nearest Integer)

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Solution

Given: $\to F = 4^i + 3^j + 4^k$

Position of intersection point where force is applied, ${\to r}_{B} = 2^i$

Point about which torque to be calculated, ${\to r}_{A} = 2^i + 3^j + 4^k$

Now, from figure ${\to r}_{A} + \to r = {\to r}_{B}$

$\to r = {\to r}_{B} - {\to r}_{A}$

$\to r = (- 3^j - 4^k)$

We know that,

$\to τ = \to r \times \to F$

$\to τ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 0 & - 3 & - 4 4 & 3 & 4 \end{matrix} ∣ ∣ ∣ ∣ ∣$

$= - 16^j - 12^k = \sqrt{(- 16)^{2} + (- 12)^{2}}$

$= \sqrt{400} = 20$

Correct Answer: $20$

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