Which of the following vectors are orthogonal to (2,1)? check all that apply.
a. (1,-2)
b. (-3,6)
c. (1,2)
d. (-2,-3)

A. (1,-2)

B. (-3,6)

Step-by-step 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