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

\to A = 2 ˆ i + 4 ˆ j - 7 ˆ k

\to B = 4 ˆ i - 6 ˆ j + 4 ˆ k

a = i - 2 j + 3 k, b = 3 i - 6 j + 9 k

a = - 2 i - 4 k, b = i - 2 j - k, c = i - 4 j + 3 k

\to F = (2 ˆ i - 3 ˆ j + 4 ˆ k) N

\to r = (3 ˆ i + 2 ˆ j + 3 ˆ k) m

2 \hat{i} + 2 \hat{j} - \hat{k}

6 \hat{i} - 2 \hat{j} - 3 \hat{k}

3 \hat{i} - 4 \hat{k}

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