Scalar And Vector Quantities - SS1 Physics Past Questions and Answers - page 5

Given:

Magnitude of velocity (V) = 20 m/s

Angle with the x-axis (θ) = 30 degrees

 

To find the x and y components, we can use the trigonometric relationships:

Vx = V X cos(θ)

Vy = V X sin(θ)

 

Calculating the components:

Vx = 20 m/s X cos(30 degrees) = 20 m/s X 0.866 = 17.32 m/s

Vy = 20 m/s X sin(30 degrees) = 20 m/s X 0.5 = 10 m/s

The x component of the velocity vector is 17.32 m/s, and the y component is 10 m/s.

 

The dot product of two vectors A and B is given by the formula: A · B = Ax X Bx + Ay X By + Az X Bz

A · B = (3 * -1) + (-2 * 4) + (5 * 2)

      = -3 - 8 + 10

      = -1

The dot product of vectors A and B is -1.

The cross product of two vectors A and B is given by the formula: A × B = (Ay X Bz - Az X By, Az X Bx - Ax X Bz, Ax X By - Ay X Bx)

A × B = [(-3 X -2) - (4 X 5), (4 X 1) - (2 X -3), (2 X 5) -( -3 X 1)]

      = [(6 - 20, 4 - (-6), 10 - (-3)]

      = (-14, 10, 13)

The cross product of vectors A and B is (-14, 10, 13).