If a- b- c- d- are the position vectors of the points A- B- C- D respectively such that 3a-5b-3c-5d-0 then AB intersects CD in the ratio

The correct option is D 5:3 Solving the equation 3 a + 5 #160;b = 3 #160;c + 5 d ∴ #160; 3 a + 5 #160;b3 + 5 = #160;3 c + 5 #160 ...

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Standard XII

Mathematics

Section Formula

If a⃗, b⃗, ...

Question

If $\to a, \to b, \to c, \to d$ are the position vectors of the points $A, B, C, D$ respectively such that $3 \to a + 5 \to b - 3 \to c - 5 \to d = 0$ then $A B$ intersects $C D$ in the ratio

2 : 3

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3 : 2

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3 : 5

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5 : 3

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Solution

The correct option is D $5 : 3$
Solving the equation
$3 ¯ ¯ ¯ a + 5 ¯ ¯ b = 3 ¯ ¯ c + 5 ¯ ¯ ¯ d$
$∴$ $\frac{3 ¯ ¯ ¯ a + 5 ¯ ¯ b}{3 + 5} = \frac{3 ¯ ¯ c + 5 ¯ ¯ ¯ d}{3 + 5}$
We see that there is a point such that it's dividing $A B$ as well as $C D$ in the above format, thus its equivalent to say that $A B$ divides $C D$ in the ratio $5 : 3$ internally.

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If →a,→b,→c,→d are the position vectors of the points A,B,C,D respectively such that 3→a+5→b−3→c−5→d=0 then AB intersects CD in the ratio

The correct option is D 5:3Solving the equation3¯¯¯a+5¯¯b=3¯¯c+5¯¯¯d∴ 3¯¯¯a+5¯¯b3+5=3¯¯c+5¯¯¯d3+5We see that there is a point such that it's dividing AB as well as CD in the above format, thus its equivalent to say that AB divides CD in the ratio 5:3 internally.

If $\to a, \to b, \to c, \to d$ are the position vectors of the points $A, B, C, D$ respectively such that $3 \to a + 5 \to b - 3 \to c - 5 \to d = 0$ then $A B$ intersects $C D$ in the ratio