Which of the following is a vector quantity?

Discipline: Physics

Academic Level: Undergrad. (yrs 3-4)

Paper Format: APA

Pages: 1 Words: 275

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Question

Which of the following is a vector quantity? speed time force displacement temperature momentum velocity acceleration The sum of two vectors is the largest when the two vectors are. pointing in the same direction pointing in opposite directions perpendicular to each other positioned at a 45 degree angle

Expert Answer

The scalars are the quantities that are explained only by the magnitude.

Hence, the incorrect options are,

• Speed

• Time

• Temperature

The speed, time and temperature have no direction. They have only magnitude. Hence, they are scalar quantities.

Vectors are the quantities that are explained by both magnitude and direction.

The force, momentum, displacement, velocity, and acceleration have both magnitude and direction. Hence, the correct options are,

• Force

• Displacement

• Momentum

• Velocity

• Acceleration

Force, displacement, momentum, velocity, and acceleration are vector quantities.

The scalars are the quantities that are explained only by the magnitude. The velocity is a vector quantity. The momentum and acceleration depend on the velocity. Hence, they are also vector quantities.

The force is directly proportional to acceleration. Hence, the force is a vector quantity.

The incorrect options are,

• Pointing in opposite direction.

• Perpendicular to each other.

• Positioned at a $4 5^{\circ}$ angle.

The expression for resultant of vector is given below:

$R = ∣ A ∣^{2} + ∣ B ∣^{2} + 2 ∣ A ∣ ∣ B ∣ cos θ$

When the two vectors are in opposite direction substitute $18 0^{\circ}$ for $θ$ .

$R = ∣ A ∣^{2} + ∣ B ∣^{2} + 2 ∣ A ∣ ∣ B ∣ cos (180)$

= ∣ A ∣^{2} + ∣ B ∣^{2} - 2 ∣ A ∣ ∣ B ∣

$= A - B$ …… (1)

If the vectors are in opposite direction, then the resultant vector is the difference in magnitude of the two vectors.

If the two vectors are perpendicular substitute $9 0^{\circ}$ for $θ$ .

$R = ∣ A ∣^{2} + ∣ B ∣^{2} + 2 ∣ A ∣ ∣ B ∣ cos (90)$

= ∣ A ∣^{2} + ∣ B ∣^{2}

…… (2)

If the two vectors are positioned at angle $4 5^{\circ}$ substitute $4 5^{\circ}$ for $θ$ .

$R = ∣ A ∣^{2} + ∣ B ∣^{2} + 2 ∣ A ∣ ∣ B ∣ cos (45)$

= ∣ A ∣^{2} + ∣ B ∣^{2} + 2

∣ A ∣ ∣ B ∣

…… (3)

When the two vectors are in same direction substitute $0^{\circ}$ for $θ$ .

$R = ∣ A ∣^{2} + ∣ B ∣^{2} + 2 ∣ A ∣ ∣ B ∣ cos (0)$

= ∣ A ∣^{2} + ∣ B ∣^{2} + 2 ∣ A ∣ ∣ B ∣

$= A + B$ …… (4)

If the two vectors are parallel then the resultant vector is the sum of two vectors. Thus, the sum of the two vectors is largest when the vectors are in same direction.

From the above equations (1), (2), (3), and (4) we get the correct option,

• Pointing in the same direction.

The sum of the two vectors is largest when the vectors are pointing in the same direction.

When the vectors are pointing in same direction, the angle between them is zero.

For the two vectors pointing in the opposite direction the angle between them is $18 0^{\circ}$