Question:
If [a×b b×c c×a ]=k [a b c]*2 then what is value of k.here a b &c are vectors?
Answer:
We know that
[a*b b*c c*a] = (a*b).[(b*c)*(c*a)]
Now, let d = b*c
So, (b*c)*(c*a) = d*(c*a)
= (d.a)c - (d.c)a
= {(b*c).a}c - {(b*c).c}a
= [b c a]c - [b c c]a
= [b c a]c {since [b c c] = 0}
= [a b c]c {since [b c a] = [c a b] = [a b c]}
Now, (a*b).[(b*c)*(c*a)] = (a*b).{[a b c]c}
= {(a*b).c}[a b c]
= [a b c][a b c]
= [a b c]2
=> [a*b b*c c*a] = [a b c]2 ................1
Given, [a*b b*c c*a] = k[a b c]2 ...............2
From equation 1 and 2, we get
k = 1
So, the value of k is 1
Not what you are looking for? Go ahead and submit the question, we will get back to you.
