Calculating the Magnitude of Vector CD Using the Cosine Rule

[erpoi]

C, D are points defined by position vectors c and d. Magnitude of c is 5, mag of d is 7, c dotproduct d is 4 ie c.d = 4, find the magnitude of vector CD.

So i started this way

c.d = magc*magdcos@
= 35cos@, @ = 83.4 degrees

But still no idea how do get magnitude of vector cd. Thank you!

 

[cristo]

Are you sure it isn't the magnitude of vector CD? (i.e. the vector from point C to point D)? If so, use the cosine rule on the triangle, since you know two vectors and an angle.

 

[erpoi]

oops yes you are right, ok i use the cos rule and do get an answer(which is correct), but I am after it as an exact value (root66). How would i get that? Thanks!

 

[HallsofIvy]

?? You say you got an answer but you want an exact value? Did you use a calculator to get $cos(\theta)$. Since you want to use $cos(\theta)$ in the cosine rule, why not just use $cos(\theta)= \frac{4}{35}$ rather than finding $\theta$ itself?