Given two vectors p and q,
(a) write an algebraic expression for the unit vector in the direction of 3p + 2q;

Question

Given two vectors p and q,
(a) write an algebraic expression for the unit vector in the direction of 3p + 2q;

mathmate · Answer

Divide any vector P by its magnitude |P| to get a unit vector.

anonymous · Answer

$$\frac{ 3p+2q }{ \sqrt{(3p+2q)^{2}} }$$

anonymous · Answer

would that  =1

mathmate · Answer

Not really, p and q are vectors, so p= q= 3p+2q=<3a+2c, 3b+2d> and magnitude of 3p+2q |3p+2q| = |<3a+2c, 3b+2d>| =sqrt((3a+2c)^2+(3b+2d)^2)

anonymous · Answer

ok , seems good. thanks!

mathmate · Answer

In summary, if $ \textbf{P}= $ and $ \textbf{Q}= $, then $3 \textbf{ P}+2\textbf{ Q} = <3a+2c, 3b+2d> $ $ \bf{ } $ and a unit vector along $3 \textbf{ P}+2\textbf{ Q}$ is $$ \frac{<3a+2c, 3b+2d>}{\sqrt{(3a+2c)^2+(3b+2d)^2}} $$

anonymous · Answer

thanks, part two of the question is : write expression for the vector that has lenght 5 and is in opposite direction to 3p + 2q

mathmate · Answer

Multiply the previous unit vector by -5 and you'll get the required vector, since the magnitude of a unit vector is 1, and the negative sign will change it to the opposite direction.