Question

Who is helping solve? I am reviewing for a final.Vector v has a magnitude of 80 and a direction 8 = 60°. What are the magnitude and direction of 4v?

Answer 1

The magnitude of vector 4v is 320, and its direction remains unchanged at 60 degrees.

Step-by-step explanation:

The problem presented involves vector multiplication and requires knowledge of how scalar multiplication affects vectors in terms of magnitude and direction. In this case, multiplying vector v by 4 only changes its magnitude, not its direction. The original vector v has a magnitude of 80 and a direction angle of 60°. When we multiply vector v by 4, the magnitude of the new vector, called 4v, becomes 4 times greater, which in this case is 320. However, the direction angle remains the same because scalar multiplication does not affect the direction of the vector unless the scalar is negative, which is not the case here. Therefore, the direction of vector 4v is still 60°.

Answer 2

Given:

Vector "v"

Magnitude = 80

Angle = 60 degree

Find-:

Magnitude and direction of 4v.

Explanation-:

Vector v

`\begin{gathered} \text{ Magnitude }=80 \\ \theta(\text{ Angle\rparen}=60 \end{gathered}`

For Vector 4V direction is the same but the magnitude will change.

`\begin{gathered} \text{ For Vector }4V \\ \\ \theta=60 \\ \\ \text{ Magnitude }=4(\text{ Magnitude of vector V\rparen} \\ \\ =4*80 \\ \\ =320 \end{gathered}`

Magnitude and direction is:

`320;60`