# Find the magnitude and direction angle of the vector v.?

v = 3(cos 100°i + sin 100°j)

||v|| =?

θ =?

how do i solve this? please show steps i do not understand it

Relevance

||v|| = 3

θ = 100°

No calculation is needed.

To understand this you have to understand components.

A vector v with magnitude ||v|| and direction θ has:

x component = ||v||cos(θ)

y component = ||v||sin(θ)

So in component form the vector is written as:

v = ||v||cos(θ)i + ||v||sin(θ)j

which is the same as:

v = ||v|| (cos(θ)i + sin(θ)j)

Matching this, term by term, to v = 3(cos(100°)i + sin(100°)j) it is clear that ||v|| = 3 and θ = 100°.

If you don't know how to resolve a vector into components, it's covered from the basics in the video in the link.

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• Your angle is 100 degrees

The x-component is 3 * cos(100)

The y-component is 3 * sin(100)

The magnitude is sqrt(x^2 + y^2) = sqrt(9 * cos(100)^2 + 9 * sin(100)^2) = sqrt(9) * sqrt(cos(100)^2 + sin(100)^2) = 3 * sqrt(1) = 3 * 1 = 3

So, if you see this form:

v = R * (cos(t)i + sin(t)j)

Then the magnitude is R and the angle is t. The math is already done for you.

• so the magnitude is 3 and the angle is 100?

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