The vector, v, is multiplied by a scalar as shown below. In which quadrant will the terminal point of the prod

Question

The vector, v, is multiplied by a scalar as shown below. In which quadrant will the terminal point of the product vector be??
v = -i + j
-3v
Looking for the quadrant of the terminal point of the product vector.

Need help setting this type of problem up and solving it. Thanks for any help.

Answer 1

v has a negative x-component and a positive y component, so it's in the 2nd quadrant.

Multiplying it by a negative scalar will result in a positive x-component and a negative y-component, so the resulting vector will be in the 4th quadrant.

-3(-i + j) = 3i - 3j

Answer 2

The vector v has both effective x and y aspects, so it lies in Quadrant I. Multiplying vector v by technique of a good scalar makes the vector longer, notwithstanding it is going to nonetheless proceed to be in Quadrant I. notwithstanding, multiplying vector v by technique of a adverse scalar flips the direction by technique of one hundred eighty ranges and makes the vector lie in Quadrant III on the grounds that now both aspects of v will be adverse. therefore, the answer is Quad I if v is accelerated by technique of a postive scalar, and Quad III if v is accelerated by technique of a adverse scalar.

Answer 3

You have 2 operators
First v vector is reversed
- v = i - j
Then multiply by scalar 3
-3v = 3i - 3j

Move 3 units along positive i-axis (x-axis) and then move 3 units along negative j-axis (negative y-axis)
Quadrants are counted anti-clockwise
So you are in 4th quadrant

Answer 4

I am imagining +i pointing right and +j pointing up (your milleage may vary)

then v points left and up and -3v will point right and down.

1) determine which directions are positive for i, j, etc. (if you have more dimensions)

2) determine the direction of your vector (here it is negative relative to i and positive relative to j).

3) multiplying the vector by a positive scalar does not change its direction; multiplying by a negative scalar reverses its direction

Answer 5

-3v =3i-3j Its components or cordinates are (3,-3,0)With x positive =3 and y negative -3 The terminal point is in the fourth cuadrant of the xy plane