Find the Unit Vector in the Direction of 3 ^ I + 4 ^ J − 12 ^ K . - Mathematics

प्रश्न

Find the unit vector in the direction of $3 \hat{i} + 4 \hat{j} - 12 \hat{k} .$

उत्तर

Let $\vec{a} = 3 \hat{i} + 4 \hat{j} - 12 \hat{k} .$
Then,
$| \vec{a} | = \sqrt{3^{2} + 4^{2} + {(- 12)}^{2}} = \sqrt{9 + 16 + 144} = \sqrt{169} = 13$
So, a unit vector in the direction of $\vec{a}$ is given by

\hat{a} = \frac{\vec{a}}{| \vec{a} |} = \frac{1}{13} (3 \hat{i} + 4 \hat{j} - 12 \hat{k}) = \frac{3}{13} \hat{i} + \frac{4}{13} \hat{j} - \frac{12}{13} \hat{k}

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Magnitude and Direction of a Vector

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Q 2 Q 1 Q 3

अध्याय 23: Algebra of Vectors - Exercise 23.6 [पृष्ठ ४८]

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अध्याय 23 Algebra of Vectors
Exercise 23.6 | Q 2 | पृष्ठ ४८

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Find the Unit Vector in the Direction of 3 ^ I + 4 ^ J − 12 ^ K . - Mathematics

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Find the Unit Vector in the Direction of 3 ^ I + 4 ^ J − 12 ^ K . - Mathematics

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