Question

If three vectors a b c form a triangle such that a=b+c

Answer 1

Answer:

Given that a = b+c

Hence, pi+qj+rk = (s+3)i + 4j + 2k

Therefore, p= s+3, q=4, r=2

Now, a= (s+3)i + 4j +2k

Area of the triangle = 1/2 |a X b|= 5(6)1/2 ---> [1]

We find that, a X b = 10i - (2s+12)j + (9-s)k

Substituting in [1]

=>1/2 [ 102 + (2s+12)2 + (9-s)2]1/2 = 5(6)1/2

=>[ 102 + (2s+12)2 + (9-s)2]1/2  = 10(6)1/2

{Square on both sides and expand}

100 + 5s2 + 30s + 225 = 600

=>5s2 + 30s + 275 = 0

=>s2 + 6s + 55 = 0

(s-5)(s+11) = 0

Therefore, s=5 and s= -11

Now, we have

p=8, p=-8

q=4

r=2

s=5, s= -11

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