Question

A vector A⃗ has a length of 8.6 m and points in the negative x direction. Find the x component of the vector −3.7A⃗ .

Answer 1

Answer:

31.8 m in the positive x-direction

Explanation:

Here we have an example of multiplication of a vector by a scalar.

In order to perform this operation, we have to:

- multiply the magnitude of the vector by the scalar

- reverse the direction of the vector if the scalar is a negative number

In this problem, the original vector has a lenght of 8.6 m and it points in the negative x direction. Now we have to find the vector -3.7A, so we have:

- The magnitude is obtained by calculating the product

$(3.7)\cdot (8.6)=31.8 m$

- The direction is reversed, because the scalar is -3.7, so the new vector will point in the positive x-direction

So the final vector is 31.8 m in the positive x-direction, and therefore its x-component is also 31.8 m in the positive direction.