First slide

Vectors

Question

The three vectors $\vec{A} = 3 \hat{i} - 2 \hat{j} + \hat{k}$ , $\vec{B} = \hat{i} - 3 \hat{j} + 5 \hat{k}$ and $\vec{C} = 2 \hat{i} + \hat{j} - 4 \hat{k}$ form

Moderate

A

An equilateral triangle
B

An isosceles triangle
C

A right angled triangle
D

No triangle

Solution

$\vec{A} = 3 \hat{i} - 2 \hat{j} + \hat{k}$ , $\vec{B} = \hat{i} - 3 \hat{j} + 5 \hat{k}$ , $\vec{C} = 2 \hat{i} + \hat{j} - 4 \hat{k}$
$| \vec{A |} = \sqrt{3^{2} + {(- 2)}^{2} + 1^{2}} = \sqrt{9 + 4 + 1} = \sqrt{14}$
$| \vec{B |} = \sqrt{1^{2} + {(- 3)}^{2} + 5^{2}} = \sqrt{1 + 9 + 25} = \sqrt{35}$
$| \vec{C |} = \sqrt{2^{2} + 1^{2} + {(- 4)}^{2}} = \sqrt{4 + 1 + 16} = \sqrt{21}$
As $B = \sqrt{A^{2} + C^{2}}$ therefore ABC will be right angled trianlge.

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