If a=j-k and c=i-j-k. then the vector b satisfying a×b+c=0 and a·b=3?
-i+j–2k
2i–j+2k
i–j–2k
i+i–2k
Explanation for the correct option:
Find vector b:
Given, a=j-k and c=i-j-k
a×b+c=0 and a·b=3
Consider, a×b+c=0
⇒ a×(a×b)+a×c=0
⇒(a·b)a–(a·a)b+a×c=0
⇒ 3a–2b+a×c=0
⇒ 2b=3a+a×c
⇒ 2b=3j–3k-2i–j–k=-2i+2j-4k
∴b=-i+j-2k
Hence, Option ‘A’ is Correct.
Let a=i+j+k and c=j-k . If b is a vector satisfying a×b=c and a.b=3, then find b.