Answer:
A. (1,-2)
B. (-3,6)
Explanation:
we know that
If two vectors are orthogonal, then the dot product ( or scalar product) of the vectors is equal to zero
so
Let
a (x1,y1) and b(x2,y2)
The dot product is equal to
a.b=(x1*x2+y1*y2)
Verify each case
case A) (2,1) with (1,-2)
(2,1).(1,-2)=(2)*(1)+(1)(-2)=2-2=0
therefore
(1,-2) is orthogonal to the given vector
case B) (2,1) with (-3,6)
(2,1).(-3,6)=(2)*(-3)+(1)(6)=-6+6=0
therefore
(-3,6) is orthogonal to the given vector
case C) (2,1) with (1,2)
(2,1).(1,2)=(2)*(1)+(1)(2)=2+2=4
therefore
(1,2) is not orthogonal to the given vector
case D) (2,1) with (-2,3)
(2,1).(-2,3)=(2)*(-2)+(1)(3)=-4+3=-1
therefore
(-2,3) is not orthogonal to the given vector