Scalor product/vectors?

Question

Using the definition of the scalar product, find the angles between the following pairs of vectors.
(a) A = - 3 i + j k and B = 2 i j - 3k


(b) = 2i - 3 j k and = - 2i - j - k


(c) = - 4i + 5 j k and = 3i + 4j - k

Answer 1

One problem per question please.

The dot or scalar product for vectors u and v can be defined as:

u • v = || u || || v || cosθ
where θ is the angle between the two vectors

cosθ = (u • v) / (|| u || || v ||)
_______________

I assume you mean:

(a) A = - 3i + j + k and B = 2i + j - 3k

A = <-3, 1, 1> and B = <2, 1, -3>

A • B = <-3, 1, 1> • <2, 1, -3> = -3*2 + 1*1 + 1*(-3) = -8

|| A || = √[(-3)² + 1² + 1²) = √(9 + 1 + 1) = √11
|| B || = √[2² + 1² + (-3)²] = √(4 + 1 + 9) = √14

Now plug into the formula for cosθ.

cosθ = (u • v) / (|| u || || v ||)
cosθ = -8 / (√11 * √14) = -8/√154

θ = arccos(-8/√154) ≈ 130.14007°

Answer 2

remember the version between a vector and a scalar. A scalar is a quantity which has magnitude basically. A vector would have the two magnitude and a path of shuttle. In Electromagnetism, an occasion of a scalar quantity may well be electric powered potential. A vector quantity may well be an electric powered field, which might have some capability (magnitude) and path. in case you think approximately the definition of the two, it is going to likely be user-friendly to work out that electric powered present day is a vector quantity. lots of the time, although, you will see present day without the vector notation (as a scalar) because of the fact the path of shuttle is dictated by way of the form of the cord it travels in. in case you have been to contemplate a planar present day, it would would desire to be seen as a vector.