Trigonometry Dot Product Question?

The norm of <x,y>, denoted |<x,y>|, is supposed to represent the length or strength of the vector <x,y>. Because of Pythagorean theorem reasons, this is defined to be sqrt(x^2 + y^2). Another way of expressing it is sqrt(length<x,y>|^2). Now imagine a right triangle with sides x and y. Then x^2 + y^2 = z^2, where z is the hypotenuse. The hypotenuse is the length we want, so we get sqrt(z^2) = sqrt(x^2 + y^2).

For your problem. |(-3,2)| = sqrt(3^2+2^2) = sqrt(9+4) = sqrt(13). The other term is |<4,5>| = sqrt(4^2+5^2) = sqrt(41). You got the digits turned around the wrong way.

|<-3,2>| = sqrt(3*3 + 2*2) = sqrt(9 + 4) = sqrt(13)

|<4,5>| = sqrt(4*4 + 5*5) = sqrt(16 + 25) = sqrt(41)

The should be the norm value.

The length of vector v is ||v||=sqrt(v1^2+v2^2+...vn^2).

So ||<-3,2>||=sqrt((-3)^2+(2)^2) =sqrt(9+4)=sqrt(13)

and

||<4,5>||=sqrt(4^2+5^2) =sqrt(16+25) =sqrt(41) .... you sure it is s'posed to be sqrt(14)?

The bars on the bottom mean magnitude of a vector. The magnitude of vectro<x,y> = sqrt(x^2 + y^2)

it relies upon, i wager, on the scope of your subject at this aspect. (a.b) supplies a huge style as its answer. a consistent huge style could have a dot product with c, if it is what your syllabus helps.