Question

Let v=<3,-1>, and w= <1,2>. Sketch the vectors v,w,v-w, and 2v+w, and also find a unit vector in the direction of v.

Answer 1

Answer with explanation:

We can write the vectors such that:

v= 3i-1j

w= 1i+2j

v-w =3i-1j-1i-2j

X= v-w = 2i-3j = <2,-3>

2v= 2(3i-1j)=6i-2j

2v+w=6i-2j+1i+2j

Y = 2v+w= 7i = <7,0>

Unit vector in direction of v =
`(<3,-1>)/(|v|)`

|v|=
`\sqrt{3^(2)+1^(2)} =√(10)`

Unit vector in direction of v =
`(<3,-1>)/(√(10) )=(3i)/(√(10))-(1j)/(√(10))`

The sketches of v, w , v-w and 2v+w are attached.

In the graph Y is 2v+w and X is v-w

Answer 2

Explanation:

First write out the vector and do the computation.

After that sketch the vector on the graph the arrow show where the vector is pointing to.

You can use the vector v to find the unit vector