I'll assume the first vector to be (5,-1).
Answer:
The vectors are not orthogonal
Step-by-step explanation:
Two vectors are orthogonal if the angle between them is 90°.
An easy test consists of calculating their dot product. If it results zero then the vectors are perpendicular or orthogonal.
Recall the dot product between two vectors x(a,b) and y(c,d) is:
[tex]\vec x\cdot \vec y=|\vec x|.|\vec y|.cos\alpha[/tex]
Also:
[tex]\vec x\cdot \vec y=a.c+b.d[/tex]
Where [tex]\alpha[/tex] is the angle between the vectors. If the angle is 90°, then cos 90° =0, and the dot product is 0.
Let's test if the vectors (5,-1) (4,32) are orthogonal:
[tex]\vec x\cdot \vec y=5*4+(-1)*(32)=20-32=-12[/tex]
Since the dot product is not zero, the vectors are not orthogonal
