Prove that the points whose position vectors are 5a-6b-7c- 7a-8b-9c- 3a-20b-5c- are collinear-

Let the points be P,Q,R. P⃗Q⃗=(7a⃗ 8b⃗+9c⃗) (5a⃗+6b⃗+7c⃗)=2a⃗ 14b⃗+2c⃗ P⃗R⃗=(3a⃗+2b⃗+5c⃗) (5a⃗+6b⃗+7c⃗)= 2a⃗+14b⃗ 2c⃗ So, P⃗Q⃗= P⃗R⃗ ∴ Poin ...

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Prove that th...

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Prove that the points whose position vectors are $5 \to a + 6 \to b + 7 \to c, 7 \to a - 8 \to b + 9 \to c, 3 \to a + 20 \to b + 5 \to c$ are collinear.

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If \to a and \to b

(3 \to a + 2 \to b) \cdot (5 \to a - 6 \to b) =

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

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

\to a, \to b, \to c

2 \to a + 7 \to b + 5 \to c = \to 0

2 \to a + 3 \to b - \to c, \to a - 2 \to b + 3 \to c, 3 \to a + 4 \to b - 2 \to c a n d \to a - 6 \to b + 6 \to c

\to a, \to b a n d \to c

7 \to a - \to c

\to a + 2 \to b + 3 \to c

- 2 \to a + 3 \to b + 5 \to c

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