Answer: PQ(3t-7,2t+4,t+4)
Let the initial point "P" of vector "u~"be "(x, y, z)", and "Q(-7,4,4)", thus for
"u=PQ," where coordinates of "PQ" are computed as the difference of corresponding coordinates of "Q" and "P" , we get
"u=(-7-x,4-y,4-z)." Vectors in the opposite direction must be (negative) scalar multiples of each other. So we need "PQ=-t\\cdot\\upsilon", where "t" is a scalar "(>0)".
There is an infinite number of choices; let's pick "t" , then "PQ=-t\\cdot\\upsilon", where "\\upsilon=(3,2,1)",
so "-7-x=-3t, 4-y=-2t, 4-z=-t"
OR: "x = 3t-7, y = 2t+4, z =t+4." So vector "PQ" with initial points "P(3t-7, 2t+4, t+4)" will be in the opposite direction to "\\upsilon" .
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