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

The unit vector in the given direction can be calculated as nbsp; nbsp; nbsp;=A→+B→A→+B→ nbsp; nbsp; nbsp;=(2i^+4j^ 7k^)+(4i^ 6j^+4k^)(2i^+4j^ 7k^) ...

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Byju's Answer

Standard XI

Mathematics

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

The correct option is C $\frac{6 ˆ i - 2 ˆ j - 3 ˆ k}{7}$
The unit vector in the given direction can be calculated as
$= \frac{\to A + \to B}{(\to A + \to B ∣ ∣ ∣} = \frac{(2 ˆ i + 4 ˆ j - 7 ˆ k) + (4 ˆ i - 6 ˆ j + 4 ˆ k)}{((2 ˆ i + 4 ˆ j - 7 ˆ k) + (4 ˆ i - 6 ˆ j + 4 ˆ k) ∣ ∣} = \frac{6 ˆ i - 2 ˆ j - 3 ˆ k}{\sqrt{6^{2} + (- 2)^{2} + (- 3)^{2}}} = \frac{6 ˆ i - 2 ˆ j - 3 ˆ k}{7}$

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Similar questions

Q. 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

\to A = 2 ˆ i + 4 ˆ j + 4 ˆ k

and

\to B = 4 ˆ i + 2 ˆ j - 4 ˆ k

are two vectors. The angle between them will be

Q. The vectors

2 ˆ i - 3 ˆ j + 4 ˆ k

and

- 4 ˆ i + 6 ˆ j - 8 ˆ k

are collinear.

Q. Show the each of the following triads of vectors are coplanar:
(i)

\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}

(ii)

\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}

(iii)

\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}

Q. Write a unit vector in the direction of the sum of the vectors

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

and

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

. [CBSE 2014]

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The unit vector in the direction of sum of the vectors →A=2ˆi+4ˆj−7ˆk and →B=4ˆi−6ˆj+4ˆk will be

The correct option is C 6ˆi−2ˆj−3ˆk7The unit vector in the given direction can be calculated as =→A+→B(→A+→B∣∣∣ =(2ˆi+4ˆj−7ˆk)+(4ˆi−6ˆj+4ˆk)((2ˆi+4ˆj−7ˆk)+(4ˆi−6ˆj+4ˆk)∣∣ =6ˆi−2ˆj−3ˆk√62+(−2)2+(−3)2 =6ˆi−2ˆj−3ˆk7

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