# Vector in Component

• May 3rd 2008, 07:02 PM
Fibonacci
Vector in Component
For this question, p=0.6i-aj, q=bi+cj, r=di+ej and s=fi+gj
find the possible values of a b c d e f and g given that

• p is a unit vector and a is a positive constant
• q is in the same direction as p and 5 times the magnitude
• r+2q=11i-20j
• s is in the same direction as r but equal in magnitude to q
thnx
• May 3rd 2008, 07:55 PM
Reckoner
Hi, Fibonacci. What have you tried so far? Do you know how to find the magnitude (norm) of a vector? If so, you can use the conditions given to form a set of equations.

Let me get you started:
We are told that $\displaystyle p=0.6\textbf{i}-a\textbf{j}$, where $\displaystyle p$ is a unit vector, which means its magnitude is 1, and $\displaystyle a$ is positive.

Since $\displaystyle \lVert p\rVert = 1$, we have

$\displaystyle \lVert p\rVert = \sqrt{0.6^2+a^2} = 1$

$\displaystyle \implies \sqrt{0.36+a^2} = 1$

Square both sides:

$\displaystyle 0.36+a^2 = 1\implies a^2 = 0.64$

$\displaystyle \implies a=\pm\sqrt{\frac{64}{100}}=\pm\frac{4}{5}$

And since $\displaystyle a>0$, you can discard the negative solution. Does that help?
• May 3rd 2008, 08:07 PM
Fibonacci
yes, i'll try and see if i can work out the other part of the question now

thank u