Question 1. Determine the vector x,
which satisfies the equation 2(x+u)=3v+(0,0,5),
where u=(1,-3,0), v=(0,2,1).
a)x=(-1,12,8)
b)x=(-2,12,8)
c)x=(-1,6,4)
d)x=(-1,0,4)
e)x=(-1,3,4)
Question 2.
Given the straight line X=[-2,-1]+t(1,3), t∈ℝ.
Determine for which values of a parameter t
the points of the straight line are within the first quadrant.
a)t∈⟨2,∞)
b)t∈⟨13,2⟩
c) For none t.
d)t∈⟨13,∞)
e)t∈(-∞,13⟩
Question 3.
Compute the distance of point A=[0,1,0]
from the intersection of planes x+y-z-7=0, 2x+3y-2z-13=0.