Vector Review

Front

What is the magnitude of the vector p = <3, -9>?

Back

9.5

Front

For two vectors, u and v, does u ⋅ v = v ⋅ u?

Back

Yes, the dot product is commutative.

Front

What is a vector?

Back

A vector is a quantity that has both magnitude and direction.

Front

Find the component form of a vector with magnitude 10 and direction 150°.

Back

<-8.66, 5>

Front

The dot product of two vectors is a(n) _______.

Back

Scalar.

Front

What is the formula for the magnitude of a vector v = ?

Back

Front

What does the dot product of two vectors represent geometrically?

Back

The dot product represents the cosine of the angle between the two vectors multiplied by their magnitudes.

Front

If vector a = <2, 3> and vector b = <4, -1>, what is a ⋅ b?

Back

a ⋅ b = 2*4 + 3*(-1) = 8 - 3 = 5.

Front

What is the angle θ between two vectors a and b if a ⋅ b = ||a|| ||b|| cos(θ)?

Back

θ = cos^(-1)(a ⋅ b / (||a|| ||b||)).

Front

What is the unit vector in the direction of vector v = <3, 4>?

Back