If a and b are two non-zero perpendicular vectors, then a vector y satisfying equations a y =c (where, c is scalar) and a y = b is

Step-by-step solution

Since, a , b and a b are non-coplanar, hence y = a x+t b x +( a b ) z For some scalars x, t and z , Now, aligned & b = a y & b =( a a ) x+( a b ) t+ a ( a b ) z & =0 x+( a b ) t+[( a b ) a -( a a ) b ] z & [ a a =0, a b =0] & b=( a b ) t-( a a ) b z & t=0 and z= -1 | a |^2 aligned Also, aligned C & = a y = a a x+ a b t+ a ( a b ) z & =| a |^2 x+0 t+0 z & =| a |^2 x [ a b =0,( a a b )=0] aligned aligned & x= c | a |^2 & y = a x+ b t+( a b ) z & y = a c | a |^2 + b 0+( a b ) -1 | a |^2 & y = 1 | a |^2 [ a c -( a b )]