What is the direction of the vector r of t equals the vector with components 1, 1 ?

Question

What is the direction of the vector  ?

A	1
B
C
D

Answer 1

If we were to plot this vector on a graph, we'd see that it's going 1 units in the x direction and 1 units in the y direction (up 1, over 1). This makes an isosceles right triangle, whose hypotenuse is the vector itself.

In the isosceles right triangle, we know that one of the angles is 90^o. Then the other two angles have to be 45^o and 45^o.

Now we can look at the relationship of the hypotenuse/vector to the x-axis. It's sticking up at a 45^o angle. In radians, that's π/4 ! Thus we can say that the direction of the vector is π/4.