Question

How does multiplying a vector by a scalar value of 2x change the vector?

Answer 1

Recall that the direction of a vector can be seen from its slope, namely b/a.

let's take a peek at a couple of vectors, and multiply them by a scalar of 2.

hmmm say < 3 , 7 > , it has a slope of 7/3, now if we use a scalar of 2

2<3,7> => < 6 , 14 >, now, the slope of that is 14/6 which simplifies to, yeap, you guessed it, to 7/3, no change in the slope.

and say hmmmm < 11 , -2 >, slope of -2/11, let's multiply it by 2

2<11,-2> => <22 , -4 >, slope is -4/22 which simplifies to -2/11.

so, the vector's magnitude gets blown up, but the slope remains the same.