Question

Suppose that each component of a certain vector is doubled.

Part A

By what multiplicative factor does the magnitude of the vector change?

Express your answer using one significant figure.

A2 =

nothing

A1

SubmitRequest Answer

Part B

By what multiplicative factor does the direction angle of the vector change?

Express your answer using one significant figure.

θ2 =

nothing

θ1

Answer 1

A)

Let the vector be given as

= a + b + c

Magnitude of vector is given as

|| = sqrt(a² + b² + c²)

Multiplying vector by "2" both side

2 = 2a + 2b + 2c

magnitude of the new vector is given as

|2| = sqrt((2a)² + (2b)² + (2c)²)

|2| = 2 sqrt(a² + b² + c²)

|2| = 2 ||

hence we multiply by a factor of "2"

B)

multiplying a vector by a scalar factor of "2" only changes the magnitude and the direction of the vector remains the same.

So multiplicative factor in case of direction angle is "1"