If vector a=i(cap)+j(cap)+k(cap) and vector b= j(cap)-k(cap), find a vector c such that 'a' cross 'c' is vector b and - Maths - Mathematical Reasoning

Question

If vector a=i(cap)+j(cap)+k(cap) and vector b= j(cap)-k(cap),
find a vector c such that 'a' cross 'c' is vector b and 'a' dot 'c'
is 3

Ajanta Trivedi · Accepted Answer

let c=xi^+yj^+zk^
given ; a=i^+j^+k^ and b=j^-k^
a×c=ba×c=i1xj1yk1z=(z-y)i^+(x-z)j^+(y-x)k^
=j^-k^⇒z-y=0⇒y=zx-z=1⇒x=1+z
a·c=3(i^+j^+k^)·(xi^+yj^+zk^)=3x+y+z=31+z+z+z=33z=2⇒z=23x=1+23=53y=23
thus the required vector c=53i^+23j^+23k^
hope this helps you

If vector a=i(cap)+j(cap)+k(cap) and vector b= j(cap)-k(cap), find a vector c such that 'a' cross 'c' is vector b and 'a' dot 'c' is 3