Three vectors overrightarrow A = 3hat{i} - 2hat{j} + hat{k},,,overrightarrow B = hat{i} - 3hat{j} +

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3-1.Vectors

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

A

An equilateral triangle

B

Isosceles triangle

C

A right angled triangle

D

No triangle

Solution

(c) $\vec A = 3\hat i – 2\hat j + \hat k$, $\vec B = \hat i – 3\hat j + 5\hat k$, $\vec C = 2\hat i – \hat j + 4\hat k$

$|\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 A| = \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 triangle.

Standard 11

Physics

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