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Vector Component

The x,y,z c...

Question

The $x, y, z$ coordinates of two point $A$ and $B$ are given respectively as $(0, 3, - 1)$ and $(- 2, 6, 4)$ . The displacement vector from $A$ to $B$ is given by:

- 2 ˆ i + 6 ˆ j + 4 ˆ k

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- 2 ˆ i + 3 ˆ j + 3 ˆ k

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- 2 ˆ i + 3 ˆ j + 5 ˆ k

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- 2 ˆ i + 4 ˆ j + 6 ˆ k

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Solution

The correct option is C $- 2 ˆ i + 3 ˆ j + 5 ˆ k$
Given $x, y, z$ coordinates of two point A and B $(0, 3, - 1)$ and $(- 2, 6, 4)$ .
The displacement vector from A to B is given by
$\to B - \to A = (- 2) ˆ i + (3 ˆ j) + (5) ˆ k$

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Similar questions

\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}

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

¯ ¯ ¯ a \times ¯ ¯ ¯ b =

a = 2 i - 3 j + 6 k

b = 2 i + 3 j - k

λ = \frac{t h e p r o j e c t i o n o f a o n b}{t h e p r o j e c t i o n o f b o n a},

λ

2 \hat{i} - \hat{j} + \hat{k}, \hat{i} - 3 \hat{j} - 5 \hat{k} and 3 \hat{i} - 4 \hat{j} - 4 \hat{k}

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

\vec{a} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} and \vec{b} = 3 \vec{i} + 4 \vec{j} + 5 \vec{k}

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