In: Physics

# A vector has components (4,2). When the vector is multiplied by the scalar 9, how does...

A vector has components (4,2). When the vector is multiplied by the scalar 9, how does its magnitude and direction change?

## Solutions

##### Expert Solution

Let a vector be

The magnitude of this vector is given by,

And its direction is given by,

The components of the given vector is (4,2). So the vector is given by,

So the magnitude of this vector is

And its direction is given by,

Its direction is 26.56 from the positive x-axis.

When this vector is multiplies by a scalar, the new vector is,

The magnitude of this vector is

And its direction is given by,

Its direction is 26.56 from the positive x-axis.

So when the vector was multiplied with a scalar, its magnitude changed but direction didn't change.

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