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Please help me solve this asap.... the correct answer is (x+y-5) Question is attatched

Please help me solve this asap.... the correct answer is (x+y-5)
 
 
Question is attatched

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Grade:12

1 Answers

Samyak Jain
333 Points
4 years ago
Given : a + xb + yc = 0   ...(1)  and  a x b + b x c + c x a = 6(b x c)         ...(2)
To solve this question, we’ll represent a in terms of b and c since RHS in second equation is in terms of (b x c).
We will use the facts that cross product of a vector with itself is a zero vector and negative of cross product
of a vector with another vector is same as cross product of second vector with the first i.e.
a x a = 0  and  – (a x b) = (b x a)
\because a + xb + yc = 0 ,  a = – (xb + yc)
Now, a x b = – (xb + yc) x b  =  – (x(b x b) + y(c x b))  =  – y(c x b)  =  y(b x c)  [\because b x b = 0]
&  c x a = c x {– (xb + yc)} = – c x (xb + yc)  =  – (x (c x b) + y(c x c)) = – x(c x b) = x(c x b)
[\because c x c = 0]
(2) becomes  y(b x c) + b x c + x(c x b)  =  6(b x c)  i.e.  
(x + y +1)(b x c)  =  6(b x c)
Comparing coefficients of b x c on both sides, we get
(x + y +1)  =  6  \Rightarrow  x + y – 5 = 0.

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