Scalar and Vector

• 5√29
• √29
• 2√29
• 3√29

Select all the scalar quantities from the options below.

• Pressure

• Force

• Density

• Displacement

• Energy

Temperature in Kelvin is considered a scalar, even though it is associated with the direction of heat flow.

• True
• False

The ________ of a substance is a scalar quantity that measures the total amount of thermal energy it contains per unit temperature.

A constant force of 50 N is applied to push a box 10 m across a frictionless surface at an angle of 30° to the horizontal. Calculate the work done by the force on the box. Discuss why work is treated as a scalar quantity, even though it involves force and displacement (both vectors).

A vector has a magnitude of 10 units and makes an angle of 30° with the positive x-axis. What are its x and y components?

• x = 8.66, y = 5

• x = 5, y = 8.66

• x = 10, y = 0

• x = 17.32, y = 10

Consider two vectors, A and B, in a plane. Which statements about their dot product are true?

• The dot product is always a vector.

• If the vectors are perpendicular, their dot product is zero.

• The dot product depends on the cosine of the angle between the two vectors.

• The dot product can be negative if the angle between the vectors is obtuse.

When two vectors are added, the resultant vector is always longer than the longer of the two original vectors.

• True
• False

Two vectors P = 7i - 4j + 2k and Q = 2i + 3j - k are added to form a resultant vector R = P + Q. Fill in the blank for vector R: _____.

A projectile is launched with an initial velocity at an angle to the horizontal. How would you decompose its velocity vector into horizontal and vertical components, and use these components to analyze its motion? Include an explanation of how the vector projection changes throughout the trajectory and its implications for the projectile's range and height.