The position vector of the point which divides the join of points 2 a -3 b and a - b in the raito 3- 1- isa 3 a-2 b-2b 7 a-8 b-4c 3 a-4d 5 a -4

Let the position vector of the point R divides the join of points 2a 3b and a+b ∴ Position vector R =3(a+b)+1(2a 3b)/3+1 Since, the position vector of a point ...

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Standard XII

Physics

Vector Addition

The position ...

Question

The position vector of the point which divides the join of points $2 \to a - 3 \to b a n d \to a + \to b$ in the raito 3 : 1, is

(a) $\frac{3 \to a - 2 \to b}{2}$

(b) $\frac{7 \to a - 8 \to b}{4}$

(c) $\frac{3 \to a}{4}$

(d) $\frac{5 \to a}{4}$

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Solution

Let the position vector of the point R divides the join of points $2 \to a - 3 \to b a n d \to a + \to b$

$∴ Position vector R = \frac{3 (\to a + \to b) + 1 (2 \to a - 3 \to b)}{3 + 1}$

Since, the position vector of a point R dividing the line segment joining the points P and Q, whose position vector of a point R dividing the line segment joining the points P and Q, whose positioin vectors are $\to p a n d \to q$ in the ratio m : n internally , is given by $\frac{m \to q + n \to p}{m + n}$

$∴ R = \frac{5 \to a}{4}$

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The position vector of the point which divides the join of points 2→a−3→b and →a+→b in the raito 3 : 1, is (a) 3→a−2→b2 (b) 7→a−8→b4 (c) 3→a4 (d) 5→a4

The position vector of the point which divides the join of points $2 \to a - 3 \to b a n d \to a + \to b$ in the raito 3 : 1, is

(a) $\frac{3 \to a - 2 \to b}{2}$

(b) $\frac{7 \to a - 8 \to b}{4}$

(c) $\frac{3 \to a}{4}$

(d) $\frac{5 \to a}{4}$