Scalar And Vector Quantities - SS1 Physics Past Questions and Answers - page 5
A velocity vector V has a magnitude of 20 m/s and is directed at an angle of 30 degrees with the positive x-axis. Resolve the velocity vector into its x and y components.
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.
Which type of vector multiplication results in a scalar quantity?
Dot product
Cross product
Both dot product and cross product
None of the above
Which type of vector multiplication results in a vector quantity?
Dot product
Cross product
Both dot product and cross product
None of the above
The dot product of two vectors A and B is zero. What can you conclude about the angle between the two vectors?
The angle is acute.
The angle is obtuse.
The angle is right angle
The angle cannot be determined.
The cross product of two parallel vectors is:
Zero vector
Vector with magnitude equal to the product of the magnitudes of the two vectors
Vector with magnitude equal to the sum of the magnitudes of the two vectors
None of the above
The cross product of two perpendicular vectors is:
Zero vector
Vector with magnitude equal to the product of the magnitudes of the two vectors
Vector with magnitude equal to the sum of the magnitudes of the two vectors
None of the above
Calculate the dot product of vectors A = (3, -2, 5) and B = (-1, 4, 2).
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.
Calculate the cross product of vectors A = (2, -3, 4) and B = (1, 5, -2).
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).