SOLUTION: 1)In 3d-space, let v1=(0,2,1) v2=(2,1,1) v3=(1,3,-1) v4=(4,2,1). Write v4 as linear combination of v1,v2,v3. 2)let v1=(0,-4,7) and v2=(3,-2,-1) find i)length of v1 ii) v1+v2

Question 1049379: 1)In 3d-space, let v1=(0,2,1) v2=(2,1,1) v3=(1,3,-1) v4=(4,2,1). Write v4 as linear combination of v1,v2,v3.
2)let v1=(0,-4,7) and v2=(3,-2,-1)
find
i)length of v1
ii) v1+v2
iii)length of v1+v2
iv)angle between v1 and v2
v)v1.v2
vi)v1xv2
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
1.(4,2,1)=a(0,2,1)+b(2,1,1)+c(1,3,-1)
(4,2,1)=(0a+2b+c,2a+b+3c,a+b-c)
Using Cramer's rule,

.
.
.

So then,
(4,2,1)=(-5/11)*(0,2,1)+(20/11)*(2,1,1)+(4/11)*(1,3,-1)
.
.
.
2.i)
ii) V[1]+V[2]=(0+3,-4-2,7-1)=(3,-6,6)
iii)
iv) Use the dot product,

Plug in the values to get the answer.
v) From previous,
vi)

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