Assertion -Position vector of a point R- which divides the line joining the points Pi - 2 j - k and Q-i - j - k in the ratio 2 - 1 internally is -1-3i - 4-3j - 1-3k Reason- r - mb - n a-m - n

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Assertion :Po...

Question

Assertion :Position vector of a point R, which divides the line joining the points $P (ˆ i + 2 ˆ j - ˆ k)$ and $Q (- ˆ i + ˆ j + ˆ k)$ in the ratio 2 : 1 internally is $\frac{- 1}{3} ˆ i + \frac{4}{3} ˆ j + \frac{1}{3} ˆ k$ Reason: $\to r = \frac{m \to b - n \to a}{m - n}$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is C Assertion is correct but Reason is incorrect
The point R which divides the line joining the point P $(\to a)$ and Q $(\to b)$ in the ratio m : n,
$\to R = \frac{m \to b + n \to a}{m + n}$
$\Rightarrow m = 2, n = 1, \to a = ˆ i + 2 ˆ j - ˆ k$ and $\to = - ˆ i + ˆ j + ˆ k$
$∴ \to R i s \frac{2 \times (- ˆ i + ˆ j + ˆ k) + 1 \times (ˆ i + 2 ˆ j - ˆ k)}{2 + 1}$
$\to R = - \frac{1}{3} ˆ i + \frac{4}{3} ˆ j + \frac{1}{3} ˆ k$

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Assertion :Position vector of a point R, which divides the line joining the points P(ˆi+2ˆj−ˆk) and Q(−ˆi+ˆj+ˆk) in the ratio 2 : 1 internally is −13ˆi+43ˆj+13ˆk Reason: →r=m→b−n→am−n

Assertion :Position vector of a point R, which divides the line joining the points $P (ˆ i + 2 ˆ j - ˆ k)$ and $Q (- ˆ i + ˆ j + ˆ k)$ in the ratio 2 : 1 internally is $\frac{- 1}{3} ˆ i + \frac{4}{3} ˆ j + \frac{1}{3} ˆ k$ Reason: $\to r = \frac{m \to b - n \to a}{m - n}$