Assertion -If three point P-Q and R have position vector a - b - c respectively and 2 a -3 b -5 c -0- then the points P-Q-R must be collinear Reason- If three points A-B-C- AB - AC then the points A-B-c must be collinear-

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Assertion :If...

Question

Assertion :If three point $P, Q$ and $R$ have position vector $\to a, \to b, \to c$ respectively and $2 \to a + 3 \to b - 5 \to c = 0$ , then the points $P, Q, R$ must be collinear Reason: If three points $A, B, C, - - \to A B = λ - - \to A C$ then the points $A, B, c$ must be collinear.

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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
$R :$ For three point $A, B, C$ if $- - \to A B = λ - - \to A C,$ then the three points are collinear $(T r u e)$
$A :$ Since $2 \to a + 3 \to b = 5 \to c \Rightarrow \frac{2 \to a + 3 \to b}{2 + 3} = \to c$
also, $2 \to a + 3 \to b = 5 \to c \Rightarrow 2 \to a + 3 \to b - 5 \to a = 5 \to c - 5 \to a \Rightarrow 3 (\to b - \to a) = 5 (\to c - \to a) \Rightarrow 3 \to A B = 5 \to A C \Rightarrow \to A B = \frac{5}{3} \to A C$
hence assertion is true and it follows
from $R$
As $- - \to A C = \to c - \to a = \frac{3}{5} (\to b - \to a)$ and $- - \to A B = \to b - \to a$
So $- - \to A B = \frac{5}{3} - - \to A C = λ - - \to A C$

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Assertion :If three point P,Q and R have position vector →a,→b,→c respectively and 2→a+3→b−5→c=0, then the points P,Q,R must be collinear Reason: If three points A,B,C,−−→AB=λ−−→AC then the points A,B,c must be collinear.

Assertion :If three point $P, Q$ and $R$ have position vector $\to a, \to b, \to c$ respectively and $2 \to a + 3 \to b - 5 \to c = 0$ , then the points $P, Q, R$ must be collinear Reason: If three points $A, B, C, - - \to A B = λ - - \to A C$ then the points $A, B, c$ must be collinear.