If $A$ , $B$ and $C$ are three collinear points, where $A = i + 8 j - 5 k$ , $B = 6 i - 2 j$ and $C = 9 i + 4 j - 3 k$ , then $B$ divides $A C$ in the ratio of :

\frac{5}{7}

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\frac{5}{3}

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\frac{2}{3}

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None of these

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Solution

The correct option is B $\frac{5}{3}$
Given points are $A (i + 8 j - 5 k)$ , $B (6 i - 2 j)$ and $C (9 i + 4 j - 3 k)$
$A B = - 5 i + 10 j - 5 k$ and $C B = 3 i + 6 j - 3 k$
$\Rightarrow \frac{| A B |}{| C B |} = \frac{\sqrt{150}}{\sqrt{54}} = \frac{5 \sqrt{6}}{3 \sqrt{6}} = \frac{5}{3}$
Therefore correct option is $B$

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Similar questions

\hat{i} + x \hat{j} + 3 \hat{k}, 3 \hat{i} + 4 \hat{j} + 7 \hat{k} and y \hat{i} - 2 \hat{j} - 5 \hat{k}

(\to A D + \to B E + \to C F) : \to C K

\to A = 2 ˆ i + 4 ˆ j - 7 ˆ k

\to B = 4 ˆ i - 6 ˆ j + 4 ˆ k

\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 = (1, 2, 3), B (3, 4, 7), C (- 3, - 2, - 5)

B

A C

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