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Section Formula

The ratio in ...

Question

The ratio in which $i + 2 j + 3 k$ divides the join of $- 2 i + 3 j + 5 k$ and $7 i - k$ is?

- 3 : 2

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1 : 2

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2 : 3

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- 4 : 3

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Solution

The correct option is B $1 : 2$
$\begin{matrix} i + 2 j + 3 k = (1, 2, 3) - 2 i + 3 j + 5 k = (- 2, 3, 5) 7 i - k = (7, 0, - 1) 1 = \frac{7 m - 2}{m + 1} m + 1 = 7 m - 2 3 = 6 m m = \frac{1}{2} S o, r a t i o i s 1 : 2 O p t i o n B i s c o r r e c t a n s w e r . \end{matrix}$

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Similar questions

\to r = (1 \to i + 2 \to j + 3 \to k) + t (- 2 \to i + \to j + \to k)

\to r = (2 \to i + 3 \to j + 5 \to k) + s (\to i + 2 \to j + 3 \to k)

- 2 \hat{i} + 3 \hat{j}, \hat{i} + 2 \hat{j} + 3 \hat{k} and 7 \hat{i} - \hat{k}

P (ˆ i + 2 ˆ j - ˆ k)

Q (- ˆ i + ˆ j + ˆ k)

\frac{- 1}{3} ˆ i + \frac{4}{3} ˆ j + \frac{1}{3} ˆ k

\to r = \frac{m \to b - n \to a}{m - n}

\to i + \to 2 j + \to 3 k

\to i - \to 2 j + \to 5 k

\to 3 j - \to 4 k

- \to 2 i + \to 3 j - \to 3 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}

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