# vectors

• September 26th 2008, 08:09 AM
Carl Feltham
vectors
Find the values of t for which the velocity of the car is parallel to the vector (i + j)

v = (3r^2 - 2t + 8)i + (5t + 6)j ms^-1

Its doing my head in not being able to work this out (Angry)
• September 26th 2008, 08:21 AM
civodul
For vectors to be parallel they need to have the same slope.

vector i+j has slope: 1/1= 1

so slope of v has to be 1 which is:

(5t+6)/(3t^2-2t+8)=1

So it is a second degree polynomial equation to solve.

civodul
• September 26th 2008, 11:41 AM
Soroban
Hello, Carl!

Quote:

Find the values of $t$ for which the velocity of the car
is parallel to the vector $\vec i + \vec j$

. . $\vec v \;= \;(3t^2 - 2t + 8)\vec i + (5t + 6)\vec j$

A vector parallel to $\vec i + \vec j$ has the form: . $\vec v \:=\:a\vec i + a\vec j$
. . That is, the coefficients are equal.

So we have: . $3t^2 - 2t + 8 \;=\;5t + 6 \quad\Rightarrow\quad 3t^2 - 7t + 2 \:=\:0$

Factor: . $(t - 2)(3t - 1) \:=\:0 \quad\Rightarrow\quad\boxed{ t \;=\;2,\:\frac{1}{3}}$

• September 26th 2008, 01:56 PM
Prove It
Quote:

Originally Posted by Carl Feltham
Find the values of t for which the velocity of the car is parallel to the vector (i + j)

v = (3r^2 - 2t + 8)i + (5t + 6)j ms^-1

Its doing my head in not being able to work this out (Angry)

Another way may be to use dot products.

Recall that

$\mathbf{a}.\mathbf{b} = |\mathbf{a}||\mathbf{b}|\cos{\theta}$.

Since the vectors will be parallel, the angle between them is 0, and so $\cos{\theta}=\cos{0} = 1$.

So in other words, in this case...

$\mathbf{a}.\mathbf{b} = |\mathbf{a}||\mathbf{b}|$

So evaluate the dot product, evaluate the product of the moduli, and solve for t.