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MathematicsVectorDot Product & Its Application ( Projection etc.)Easy2 minPYQ_2017

MathematicsEasysingle choice

The area (in sq. units) of the parallelogram whose diagonals are along the vectors $8 \hat{i} - 6 \hat{j}$ and $3 \hat{i} + 4 \hat{j} - 12 \hat{k},$ is:

Options:

Answer:

Solution:

Let the given diagonals be $\vec{d_{1}}$ and $\vec{d_{2}}$ , then

$d_{1} \times d_{2} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 8 & - 6 & 0 \\ 3 & 4 & - 12 \end{matrix}|$

$= 72 \hat{i} - (- 96) \hat{j} + 50 \hat{k}$

$|d_{1} \times d_{2}| = \sqrt{72^{2} + {(- 96)}^{2} + {(50)}^{2}} = \sqrt{5184 + 9216 + 2500}$

$|d_{2} \times d_{2}| = \sqrt{16900} = 130$

$Area = \frac{1}{2} |d_{1} \times d_{2}| = \frac{1}{2} \times 130$

$= 65$

Stream:JEESubject:MathematicsTopic:VectorSubtopic:Dot Product & Its Application ( Projection etc.)

⏱ 2mℹ️ Source: PYQ_2017

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