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Three vectors A,B,C such that A=B+C forming a triangle with an area of 5√6 units.IfA=.Find a+b+c+d, C=, B=

Three vectors A,B,C such that A=B+C forming a triangle with an area of 5√6 units.IfA=.Find a+b+c+d, C=, B=

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Grade:12th pass

1 Answers

Arun
25750 Points
3 years ago
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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