Finding components of vectors, im stuck.?

Question

You are given vectors A= 5.10 ihat −6.90 jhat and
B= −3.50ihat+ 6.90jhat. A third vector C lies in the xy-plane. Vector C is perpendicular to vector A and the scalar product of C with B is 18.0 .

Find the x-component of vector C.

Find the y-component of vector C.

Anybody know the equation?

Answer 1

well its simultaneous equations

5.10*D-6.90*E=0

-3.50*D+6.90*E=18.0

where C=D ihat + E jhat

Answer 2

C= X IHAT + Y IHAT
PERPENDICULAR, (A.C)=0=5.1X−6.9Y----EQ 1
SCALAR PRODUCT, (C.B)=18=−3.5X+6.9Y---EQ 2

EQ 1 + EQ 2=.....U GET X VALUE
REPLACE IT IN EQ 1 TO GET Y VALUE