# Finding the value of p in vectors

#### darkfenix21

First off I hope this is in the right forum I've been working on two questions both of which have been giving me trouble. The first states:

Determine "k" given two vectors and the angle between them.

vectors a=(1,1) and b=(0,k) with and angle of 45 degrees.

I was using the dot product to solve with with

a.b= lal lbl cos45

0= (sqrt 2) + kcos45

-(sqrt 2)/cos 45 =k

k=2

if anyone could tell me if I'm right that be fantastic

The second question is similar:

Find the value of "p" if the vectors r=(p,p,1) and s+(p,-2,-3) are perpendicular to each other

again i used the dot product and got

0=lal lbl cos90

0= (p)(p) +(p)(-2)+(-1)(3)

0= (p^2) -2p -3

3= (p^2) -2p

this is where I get stuck so if anyone could help me out it would be much appreciated thank you

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Hello darkfenix21
First off I hope this is in the right forum I've been working on two questions both of which have been giving me trouble. The first states:

Determine "k" given two vectors and the angle between them.

vectors a=(1,1) and b=(0,k) with and angle of 45 degrees.

I was using the dot product to solve with with

a.b= lal lbl cos45

0= (sqrt 2) + kcos45

-(sqrt 2)/cos 45 =k

k=2

if anyone could tell me if I'm right that be fantastic
I'm not sure what you mean here. The vectors $$\displaystyle \binom 1 1$$ and $$\displaystyle \binom 0 k$$ are at $$\displaystyle 45^o$$ for all positive values of $$\displaystyle k$$.

The second question is similar:

Find the value of "p" if the vectors r=(p,p,1) and s+(p,-2,-3) are perpendicular to each other

again i used the dot product and got

0=lal lbl cos90

0= (p)(p) +(p)(-2)+(-1)(3)

0= (p^2) -2p -3

3= (p^2) -2p

this is where I get stuck so if anyone could help me out it would be much appreciated thank you
$$\displaystyle p^2 -2p -3=0$$
You can do that, can't you?

#### darkfenix21

thank you very much for the help on the second question. That solution is so simple and i was over complicating it for myself :s kinda embarassing really.

as for the first question I thing I arranged the equation incorrectly and k should actually be equal to .5

as 0=lal lbl cos 45

cos45= (sqrt2)k
cos45/(sqrt 2)=k
.5=k

when subbed into the normal equation of a.b= lal lbl cos 45 as a check i get

(1)(0)+(1)(.5)= (sqrt2)(.5)cos45

.5=.5

so pretty sure it was another simple and embarassing error on my part :s