To compute (x⋅x)(x⋅w)x, we first need to calculate the dot product between vectors x and x, and between vectors x and w. Let's perform these calculations:
Dot product of x and x:
x⋅x = (6 * 6) + (-2 * -2) + (1 * 1)
= 36 + 4 + 1
= 41
Dot product of x and w:
x⋅w = (6 * 3) + (-2 * -2) + (1 * -5)
= 18 + 4 - 5
= 17
Now, we can substitute these values into the expression (x⋅x)(x⋅w)x:
(41 * 17) * x = (697) * x
Therefore, the result of (x⋅x)(x⋅w)x is 697 times the vector x.