# 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

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Question: Which of the following is a vector quantity? speed time force dis…

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General guidance

Concepts and reason The concept used to solve the problem is scalar, vector quantities, and resultant of two vectors. Initially, use the definition of scalar and vector quantities to identify the vector quantities. Finally, use the definition expression for resultant of two vectors to find the correct option.

Fundamentals The quantities are divided into two categories. They are as follows: 1.Scalar quantity. 2.Vector quantity. Scalars are the quantities that are explained only by the magnitude. Vectors are the quantities that are explained by both magnitude and direction. The expression for resultant of vector is given below: R=VA? + B2 +2 A B cose Here, the resultant is R, is the angle between the vector A and B , and the vectors are represented by A and B.

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Step-by-step

FIRST STEP ALL STEPS | ANSWER ONLY

Step 1 of 2 ^

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.

Explanation Common mistakes Hint for next step 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.

Step 2 of 2 ^

The incorrect options are, • Pointing in opposite direction. • Perpendicular to each other. • Positioned at a 45° angle. The expression for resultant of vector is given below: R=VA + B +2 |A|B|cos When the two vectors are in opposite direction substitute 180° for 0.

R=VA? + B’ +2A B cos (180)

….. (1)

= VA + B2 – 2 |A|B|

= A-B 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 90° for O.

R=VA? +B? +2 A B cos (90)

…… (2) =VA? + B12 If the two vectors are positioned at angle 45° substitute 45° for .

…..(3)

R = V141 + | Bjo +2 |A||B|cos (45)

= VA + | BR + V2|4||B|

When the two vectors are in same direction substitute 0° for 0.

R=v141 +B+2 |A||B| cos (0)

= V 42 + B

+2|A|B|

= A +B 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.

Explanation Common mistakes 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 180°.

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

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