The unit vector in the direction of sum of the vectors nbsp-A-2i-4j-7k- nbsp-and nbsp-B-4i-6j-4k- will be6i-2j-3k-i-j-k-6i-2j-3k-7

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Orthogonal System of Vectors

The unit vect...

Question

The unit vector in the direction of sum of the vectors $\to A = 2 ˆ i + 4 ˆ j - 7 ˆ k$ and $\to B = 4 ˆ i - 6 ˆ j + 4 ˆ k$ will be

6 ˆ i - 2 ˆ j - 3 ˆ k

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ˆ i - ˆ j - ˆ k

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\frac{6 ˆ i - 2 ˆ j - 3 ˆ k}{7}

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Solution

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\vec{a} = \hat{i} + 2 \hat{j} - \hat{k}, \vec{b} = 3 \hat{i} + 2 \hat{j} + 7 \hat{k}, \vec{c} = 5 \hat{i} + 6 \hat{j} + 5 \hat{k}

\vec{a} = - 4 \hat{i} - 6 \hat{j} - 2 \hat{k}, \vec{b} = - \hat{i} + 4 \hat{j} + 3 \hat{k}, \vec{c} = - 8 \hat{i} - \hat{j} + 3 \hat{k}

\hat{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \hat{b} = - 2 \hat{i} + 3 \hat{j} - 4 \hat{k}, \hat{c} = \hat{i} - 3 \hat{j} + 5 \hat{k}

\vec{a} = 2 \hat{i} + 2 \hat{j} - 5 \hat{k}

\vec{b} = 2 \hat{i} + \hat{j} - 7 \hat{k}

\vec{a} = \hat{i} + 4 \hat{j} + 2 \hat{k}, \vec{b} = 3 \hat{i} - 2 \hat{j} + 7 \hat{k} and \vec{c} = 2 \hat{i} - \hat{j} + 4 \hat{k} .

\vec{d}

\vec{a} and \vec{d}

and \vec{c} \cdot \vec{d} = 15 .

2 \hat{i} + \hat{j} - \hat{k}, 3 \hat{i} - 2 \hat{j} + \hat{k} and \hat{i} + 4 \hat{j} - 3 \hat{k}

3 \hat{i} - 2 \hat{j} + 4 \hat{k}, \hat{i} + \hat{j} + \hat{k} and - \hat{i} + 4 \hat{j} - 2 \hat{k}

\to A = 2 ˆ i + 4 ˆ j - 7 ˆ k

\to B = 4 ˆ i - 6 ˆ j + 4 ˆ k

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