Question

Determine the cosine of the angle between the vectors u = 2i - 3j - 2k and v = i + 3j - k.

Answer 1

Just use the identity \[\frac{u \cdot v}{|u||v|}=\cos{\theta}\]

Answer 2

u.v = mod u * mod v cos ( angle )

Answer 3

Just as a question, why does that identity give cos theta?

Answer 4

Like, why does the dot product over the magnitudes = cos theta?

Answer 5

u.v = 2i-9j+2k now take mod of u.v & after take mod ofu, v & jst plug in simply

Answer 6

bcas i referred for x- axis & j- for y-axis , k - z axis , hence there must be some angle between them tats why...

Answer 7

The proof of this identity comes from projecting one of the vectors, lets say u, along the other vector v. This basically means that if you were to look at the v vector from "above", with above meaning that the u vector is always on top of the v vector, the projection is how long the u vector appears to be. This projection allows you to form a triangle, and then a simple trig calculation will finish the proof of the identity. For a nice picture, see http://en.wikipedia.org/wiki/Vector_projection Hope this helps :)