Question

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

The vector will not change direction but will decrease in magnitude
The vector will change direction and decrease in magnitude
The vector will not change direction but will increase in magnitude
The vector will change direction and increase in magnitude

Answer 1

Should be, changes the magnitude of the vector, but not the direction. Hope this helps!

Answer 2

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.