Exercise 1.2.6

Question

(A)Describe every vector w = (w1,w2) that is perpendicular to v = (2,-1)
(B) all vectors  perpendicular to v = (1,1,1) lie on a _______ in 3 dimensions
(C) The vectors perpendicular to both (1,1,1) and (1,2,3) lie on a ______.

Prakash Anand · Accepted Answer

All vectors $\boldsymbol{w}=(c, 2 c)$ are perpendicular to $\boldsymbol{v}$. They lie on a line. All vectors $(x, y, z)$ with $x+y+z=0$ lie on a plane. All vectors perpendicular to $(1,1,1)$ and $(1,2,3)$ lie on a line in $3$-dimensional space.

Exercise 1.2.6

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Exercise 1.2.6

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