Position vectors of mid point of the vector joining the points $P (2, 3, 4)$ and $Q (4, 1, - 2)$ is

2 ˆ i + ˆ j + ˆ k

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3 ˆ i + 2 ˆ j + ˆ k

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- 3 ˆ i - ˆ j + ˆ k

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None

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Solution

The correct option is B $3 ˆ i + 2 ˆ j + ˆ k$
Let $- - \to O P = 2 ˆ i + 3 ˆ j + 4 ˆ k$ and $- - \to O Q = 4 ˆ i + ˆ j - 2 ˆ k$
Let mid-point of $P Q$ be $R$
$∴ - - \to O R = \frac{- - \to O P + - - \to O Q}{2}$
$- - \to O R = \frac{6 ˆ i + 4 ˆ j + 2 ˆ k}{2}$
Hence, $- - \to O R = 3 ˆ i + 2 ˆ j + ˆ k$

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

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

Find the position vector of the mid-point of the vector joining points P(2,3,4) and Q(4,1,-2).

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

\vec{r} = 3 \hat{i} - \hat{j} - \hat{k} + λ (2 \hat{i} - 2 \hat{j} + \hat{k}) .

\to O A = i + j + k, \to A B = 3 i - 2 j + k, \to B C = i + 2 j - 2 k, \to C D = 2 i + j + 3 k

A unit vector in the plane of the vectors 2i + j + k, i - j + k and orthogonal to 5i + 2j + 6k is

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