First slide

Introduction to 3-D Geometry

Question

If the projections of the line segment $\bar{A B}$ on the coordinate planes are $2, k, 6$ and $A B = 6$ , then $\sqrt{k^{2} - 7} =$

Easy

A

3
B

4
C

5
D

None

Solution

If $d_{1}, d_{2}, d_{3}$ are the projections of the line segment of length $d$ on the coordinate planes then ${d_{1}}^{2} + {d_{2}}^{2} + {d_{3}}^{2} = 2 d^{2}$
$\begin{array}{l} \Rightarrow 2^{2} + k^{2} + 6^{2} = 2 {(6)}^{2} \\ \Rightarrow 4 + 36 + k^{2} = 72 \\ \Rightarrow k^{2} = 32 \end{array}$
Therefore, $\sqrt{k^{2} - 7} = 5$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App