vector problem!

**iExcavate** · January 15th 2010, 09:32 PM

i apologise if this is the incorrect forum, i assume it would go under here or perhaps calculus forum - vector help!

find the formula for $||b -a||^2$ in terms of $||b||^2$ , $||a||^2$ and $b·a$

thankyou so much in advance!

**tonio** · January 15th 2010, 11:13 PM

Originally Posted by iExcavate

i apologise if this is the incorrect forum, i assume it would go under here or perhaps calculus forum - vector help!

find the formula for $||b -a||^2$ in terms of $||b||^2$ , $||a||^2$ and $b·a$

thankyou so much in advance!

This question belongs, me believes ,in trigonometry-analytic geometry. Anyway:

$b-a$ is an arrow beginning at $a$ and ending at $b$ and $\|b-a\|$ is its length, so using the cosines law (theorem) on the resulting triangle we get:

$\|b-a\|^2=\|a\|^2+\|b\|^2-2\|a\|\|b\|\cos \theta$

I'm not sure what is $ba$ , but if you meant the dot product of these two vectors then just remember that $\cos \theta=\frac{b\cdot a}{\|b\|\|a\|}$ , so you can substitute above.

Tonio

**iExcavate** · January 15th 2010, 11:42 PM

how do i deduce $\|b-a\|^2 = \|b\|^2 + \|a\|^2 - 2\|a\|\|b\|cos\theta$
to prove: $\cos \theta=\frac{b\cdot a}{\|b\|\|a\|}$

**HallsofIvy** · January 16th 2010, 12:49 AM

tonio told you: apply the cosine law to the triangle with sides a, b, and a- b.

Thread: vector problem!

LinkBack

Thread Tools

Display

vector problem!

Similar Math Help Forum Discussions

A vector problem.

Vector Problem

Gr 12. Vector problem!

A Vector Problem

Vector Problem

Search Tags