Mathematics - Vector Question with Solution | TestHub

MathematicsVectorDot Product & Its Application ( Projection etc.)Medium2 minPYQ_2021

MathematicsMediumsingle choice

A hall has a square floor of dimension $10 m \times 10 m$ (see the figure) and vertical walls. If the angle $G P H$ between the diagonals $A G$ and $B H$ is $\cos^{- 1} \frac{1}{5},$ then the height of the hall (in meters) is:

Options:

Answer:

Solution:

$\vec{AG} = 10 \hat{i} + h \hat{j} + 10 \hat{k}$

$\vec{BH} = - 10 \hat{i} + h \hat{j} + 10 \hat{k}$

$\cos θ = \frac{- 100 + h^{2} + 100}{{(\sqrt{200 + h^{2}})}^{2}}$

$\frac{1}{5} = \frac{h^{2}}{200 + h^{2}}$

$200 = 4 h^{2}$

$h^{2} = 50$

$\Rightarrow h = 5 \sqrt{2}$

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

⏱ 2mℹ️ Source: PYQ_2021

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