Question

1.
Statement (A): The direction of î is always along horizontal
Statemetn (B): The direction of ſ is along positive x axis
a) Both A and B are true
b) Both A and B are false
c) A is true and B is false
d) A is false and B is true​

Answer 1

Explanation:

As illustrated in (Figure), vector

→

A

is the diagonal of the rectangle where the x-component

→

A

x

is the side parallel to the x-axis and the y-component

→

A

y

is the side parallel to the y-axis. Vector component

→

A

x

is orthogonal to vector component

→

A

y

.

Vector A is shown in the x y coordinate system and extends from point b at A’s tail to point e and its head. Vector A points up and to the right. Unit vectors I hat and j hat are small vectors pointing in the x and y directions, respectively, and are at right angles to each other. The x component of vector A is a vector pointing horizontally from the point b to a point directly below point e at the tip of vector A. On the x axis, we see that the vector A sub x extends from x sub b to x sub e and is equal to magnitude A sub x times I hat. The magnitude A sub x equals x sub e minus x sub b. The y component of vector A is a vector pointing vertically from point b to a point directly to the left of point e at the tip of vector A. On the y axis, we see that the vector A sub y extends from y sub b to y sub e and is equal to magnitude A sub y times j hat. The magnitude A sub y equals y sub e minus y sub b.

Figure 2.16 Vector

→

A

in a plane in