Question

Can someone please help me with this PRACTICE quiz? VECTORS IN 3-D SPACE.

Given vector u=<5,8,-3> & vector v=<7,6-6>,
find an ordered triple that represents 3u-2v.

Find the magnitude of WX for W(-9,4,6) &
X(3,-3,6).

Find an ordered triple to represent u in each equation if v=<2,-4,4> &
w=<6,-8,9>.

a.) u=v+w b.) u=v-w

Suppose that the force acting on an object can be expressed by the vector <85,35,110>, where each measure in the ordered triple represents the force in pounds. What is the magnitude of this force? Round answer to the nearest whole integer if necessary.

Answer 1

when you scale a vector you just multiply each of its components by the scale

i.e.,

if u = <5, 8, -3> then 3u = <3 * 5, 3 * 8, 3 * -3> = <15, 24, -9>
and then when you add two vectors, you just add the components

like for example

<3, 1, 7> + <8, 0, -4> = <11, 1, 3>

to determine the magnitude of a 3D vector you just expand the distance equation of two dimensions and add an extra coordinate.

magnitude = \[\sqrt{x^{2} + y^{2} + z^{2}}\]
where x is the x coordinate, y is the y coordinate, and z is the z coordinate

Answer 2

Thank you, I greatly appreciate this but it didn't help me too much :/

Answer 3

Let's see. If we know

u = <5, 8, -3>

and

3u = <15, 24, -9>

We also know

v = <7, 6, -6>

Can you identify what -2v would be ?

Answer 4

Nevermind, I figured it out. I was just writing it down wrong. Thank you :)

Answer 5

cool. good luck with your studies!