Assertion :Line joining the points $(1, 2, 3)$ & $(2, 3, 5)$ is parallel to the line joining the points $(- 1, 2, - 3)$ & $(1, 4, 1)$ Reason: Two lines whose DR's are $(a_{1}, b_{1}, c_{1})$ & $(a_{2}, b_{2}, c_{2})$ are parallel if $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

Both Assertion & Reason are individually true & Reason is correct explanation of Assertion

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Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion

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Assertion is true but Reason is false

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Assertion is false but Reason is true

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Solution

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
Line joining the points $(1, 2, 3)$ & $(2, 3, 5)$
both are parallel to the line joining the points $(- 1, 2, - 3)$ & $(1, 4, 1)$
Thus assertion is True

Two lines whose DR's are $(a_{1}, b_{1}, c_{1})$ & $(a_{2}, b_{2}, c_{2})$ are parallel
$i . e . \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
Hence Reason also True.
$∴$ Both Assertion & Reason are individually true & Reason is correct explanation of Assertion.

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Assertion :Line joining the points (1,2,3) & (2,3,5) is parallel to the line joining the points (−1,2,−3) & (1,4,1) Reason: Two lines whose DR's are (a1,b1,c1) & (a2,b2,c2) are parallel if a1a2=b1b2=c1c2

Assertion :Line joining the points $(1, 2, 3)$ & $(2, 3, 5)$ is parallel to the line joining the points $(- 1, 2, - 3)$ & $(1, 4, 1)$ Reason: Two lines whose DR's are $(a_{1}, b_{1}, c_{1})$ & $(a_{2}, b_{2}, c_{2})$ are parallel if $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$