r(t)
=⟨−1,2,1⟩+t⟨−2,−3,1⟩
=⟨−1,2,1⟩+⟨−2t,−3t,t⟩
Adding, this gives
=⟨−1−2t,2−3t,1+t⟩
⟹x=−1−2t
y=2−3t
z=1+t
Substituting x,y,z into 3y−x+z, we have
3(2−3t)−(−1−2t)+(1+t)=−4
⟹6−9t+1+2t+1+t=−4
⟹−9t+2t+t+6+1+1=−4
⟹−6t+8=−4
⟹−6t=−4−8
⟹−6t=−12
Dividing both sides by −6 .This gives
t=−6−12=2
Substituting t into ⟨−1−2t,2−3t,1+t⟩
We have
⟨−1−2(2),2−3(2),1+2⟩
P=⟨3,−4,3⟩
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