2 Questions that maybe are related

Question

346. Write an equation that says that vectors [a, b, c] and [m, n, p] are perpendicular.

Am I to write: am+bn+cp=0, that the dot product of these two vectors are perpendicular?

345.Write an equation that says that points (0,0,0), (a,b,c), and (m,n,p) form a right triangle, the right angle being at the origin. Simplify your equation as much as you can.

I ended up with: (√a^2+b^2+c^2) * (√m^2+n^2+p^2) = -am-bn-cp

Answer 1

346) You are correct to state that the vectors are perpendicular if their dot product is 0. I think the equation you've written shows that.

345) Your expression looks good for this one as well.

Do you see the connection?

Remember that to find the angle between two vectors v and w we use

cos θ = (v (dot) w)/(||v|| ||w||)

The reason the vectors are perpendicular if the dot product is 0 is because cos^-1 (0) = 90°.

If you look at your expression.

The left side is ||v|| ||w|| - the magnitude of v if v is the vector from (0, 0, 0) to (a, b, c) and the magnitude of w is w is the vector from (0, 0, 0) to (m, n, p).

The right side is the negative of the dot product of v and w. -am - bn - cp = -(am + bn +cp)