CUET PG 2023 — Mathematics PYQ

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Question

CUET PG 2023 — Mathematics PYQ

CUET PG | Mathematics | 2023

The moment of the couple formed by the forces $5 \hat{i} + \hat{k}$ and $- 5 \hat{i} - \hat{k}$ acting at the points (9,-1,2) and (3,-2,1) respectively, is

Choose the correct answer:

Explanation

1. Position Vector ( $\vec{r}$ ) nikaalna:

Humein point B se point A tak ka vector nikaalna hai:

\vec{r} = \vec{r}_A - \vec{r}_B

\vec{r} = (9-3)\hat{\mathbf{i}} + (-1 - (-2))\hat{\mathbf{j}} + (2-1)\hat{\mathbf{k}}

\vec{r} = 6\hat{\mathbf{i}} + 1\hat{\mathbf{j}} + 1\hat{\mathbf{k}}

2. Moment of the Couple ( $\vec{M}$ ) calculate karna:

Moment ka formula hota hai:

\vec{M} = \vec{r} \times \vec{F}

Isse determinant method se solve karte hain:

\vec{M} = \begin{vmatrix} \hat{\mathbf{i}} & \hat{\mathbf{j}} & \hat{\mathbf{k}} \\ 6 & 1 & 1 \\ 5 & 0 & 1 \end{vmatrix}

3. Determinant ko expand karna:

\vec{M} = \hat{\mathbf{i}}(1(1) - 0(1)) - \hat{\mathbf{j}}(6(1) - 5(1)) + \hat{\mathbf{k}}(6(0) - 5(1))

\vec{M} = \hat{\mathbf{i}}(1) - \hat{\mathbf{j}}(1) + \hat{\mathbf{k}}(-5)

\vec{M} = \hat{\mathbf{i}} - \hat{\mathbf{j}} - 5\hat{\mathbf{k}}

Final Answer:

The moment of the couple is:

\mathbf{\hat{i} - \hat{j} - 5\hat{k}}

Choose the correct answer:

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