What is the magnitude of -2a - 3b when a=3i+9j and b=4i-6j?

Dot product of the 2 vectors = 0. Therefore cos x = 0 where j is the angle between the 2 vectors. S0 j = 90°... I believe.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4