At what value are vectors perpendicular?

[Zaiheinles]

a, m, n, b, - vectors

Given vectors a = m + n, b = m - αn, where |m| = 4, |n| = 1, (m;n) = pi/2

At what value of α will the vectors a and b be perpendicular?

How to do it?

 

[Deleted member 4993]

(m;n) = pi/2

What does that mean - please explain.

 

[pka]

a, m, n, b, - vectors
Given vectors a = m + n, b = m - αn, where |m| = 4, |n| = 1, (m;n) = pi/2
At what value of α will the vectors a and b be perpendicular?

Your notation is anything but standard. As you have been told [imath](\vec{m},\vec{n})[/imath] is not standard.
However [imath]\vec{a}\cdot\vec{b}=0[/imath] is standard notation for perpendicular vectors.
More over [imath](\vec{a}\cdot\vec{b})=(\vec{m}+\vec{n})\cdot(\vec{m}-\alpha\vec{n})=\vec{m}\cdot{m}-\alpha\vec{m}\cdot{n}+\vec{n}\cdot{m}-\alpha\vec{n}\cdot{n}[/imath]
Also recall that [imath]\vec{m}\cdot \vec{m}=\|\vec{m}\|^2[/imath]



[imath][/imath][imath][/imath][imath][/imath][imath][/imath][imath][/imath][imath][/imath]