# Thread: Some vector algebra problems.

1. ## Some vector algebra problems.

1.Find $\displaystyle \vec{a} x \vec{b}$(Vectorial product) if $\displaystyle \vec{a}=3\vec{m}+2\vec{n}$, $\displaystyle \vec{b}=\vec{m}+5\vec{n}$ and $\displaystyle |\vec{m}|=|\vec{n}|=1$. (Angle between m and n is 90 degrees.)

2.We have vectors $\displaystyle \vec{a}=(0,2\lambda,\lambda),$ $\displaystyle \vec{b}=(2,2,1)$ and $\displaystyle \vec{c}=(-1,-2,-1)$

a) Find $\displaystyle \vec{d}$ from this conditions: $\displaystyle \vec{a}x\vec{b} = \vec{c}x\vec{d}$ and $\displaystyle \vec{a}x\vec{c} = \vec{b}x\vec{d}$ (Vectorial product).
b) Prove that vectors $\displaystyle \vec{a} - \vec{d}$ and vectors $\displaystyle \vec{b} - \vec{c}$ are colinear.
c) Find $\displaystyle \lambda$ from condition $\displaystyle (\vec{a}-\vec{b})*\vec{c}=\vec{a}*\vec{c}+\lambda$

3. Write equation of normal from point $\displaystyle M(2,3,1)$ into line:$\displaystyle l: \frac{x+1}{2}=\frac{y-0}{-1}=\frac{z-2}{3}$.

Thank you.

2. The first one should go like shown below.

3. logic, it's vectorial (cross) product. Any idea for these problems?

Anyway thank you.

4. Originally Posted by GreenMile
1.Find $\displaystyle \vec{a} x \vec{b}$(Vectorial product) if $\displaystyle \vec{a}=3\vec{m}+2\vec{n}$, $\displaystyle \vec{b}=\vec{m}+5\vec{n}$ and $\displaystyle |\vec{m}|=|\vec{n}|=1$. (Angle between m and n is 90 degrees.)

[snip]
Note that m x m = n x n = 0. Nothing much can be said about m x n except that it will be another vector perpendicular to m and n and that its magnitude will be equal to 1.