Vector Algebra

Question

Find a unit vector in the direction of $\vec{a} = 3 \hat{i} - 2 \hat{j} + 6 k$

Solution

$The unit vector (\hat{a}) in the direction of \vec{a} is given by \frac{\vec{a}}{|\vec{a}|} \hat{a} = \frac{3 \hat{i} - 2 \hat{j} + 6 \hat{k}}{\sqrt{3^{2} + (- 2)^{2}} + 6^{2}} = \frac{3 \hat{i} - 2 \hat{j} + 6 \hat{k}}{\sqrt{9 + 4 + 36}} = \frac{3 \hat{i} - 2 \hat{j} + 6 \hat{k}}{\sqrt{49}} = \frac{1}{7} [3 \hat{i} - 2 \hat{j} + 6 \hat{k}] = \frac{3}{7} \hat{i} - \frac{2}{7} \hat{j} + \frac{6}{7} \hat{k}$

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.
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Vector Algebra

Find a unit vector in the direction of $\vec{a} = 3 \hat{i} - 2 \hat{j} + 6 k$

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.
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Classify the following measures as scalars and vectors.
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Classify the following measures as scalars and vectors.
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Classify the following measures as scalars and vectors.
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Classify the following measures as scalars and vectors.
work done

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Vector Algebra

Find a unit vector in the direction of a →= 3i ^ - 2j^ + 6k

Some More Questions From Vector Algebra Chapter

Classify the following measures as scalars and vectors.2 meters north-west

Classify the following measures as scalars and vectors.40°

Classify the following measures as scalars and vectors.40 watt

Classify the following measures as scalars and vectors.10–19 coulomb

Classify the following measures as scalars and vectors.20 m/s2

Classify the following measures as scalars and vectors.time period

Classify the following measures as scalars and vectors.distance

Classify the following measures as scalars and vectors.force

Classify the following measures as scalars and vectors.velocity

Classify the following measures as scalars and vectors.work done

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find a unit vector in the direction of $\vec{a} = 3 \hat{i} - 2 \hat{j} + 6 k$

Classify the following measures as scalars and vectors.
2 meters north-west

Classify the following measures as scalars and vectors.
40°

Classify the following measures as scalars and vectors.
40 watt

Classify the following measures as scalars and vectors.
10^–19 coulomb

Classify the following measures as scalars and vectors.
20 m/s²

Classify the following measures as scalars and vectors.
time period

Classify the following measures as scalars and vectors.
distance

Classify the following measures as scalars and vectors.
force

Classify the following measures as scalars and vectors.
velocity

Classify the following measures as scalars and vectors.
work done