8.6.2 – Orthogonal Vectors

At the end of yesterday, we addressed the case of using the dot product to determine the angles between vectors Similar to equations from algebra, we can talk about relationship of vectors as well – Parallel – Perpendicular – Neither

Orthogonal Two nonzero vectors u and v are said to be orthogonal (perpendicular) if Same as saying the angle ϴ is a right angle/90 degrees

When finding vectors that are orthogonal, there may be an infinite number of solutions Easiest way; pick one number with opposite sign and assign it to the first; then, find a second number such that they will add to zero – Takes some experimentation!

Example. Find a vector orthogonal to the vector u = {-6, 6}.

Example. Find a nonzero vector orthogonal to v = 2i – 4j

Example. Find two nonzero vectors orthogonal to the vector u = {-10, 3}

P,P,N To determine if vectors are parallel, perpendicular, or neither, we can use the dot product theorem from yesterday, and look for the following; – Parallel; if tan(ϴ) is the same for both vectors, then they are parallel – Perpendicular; dot product = 0 – Neither; none of the above

Example. Determine whether u and v are orthogonal, parallel, or neither. u = {2, -3} v = {-6, 9}

Example. Determine whether u and v are orthogonal, parallel, or neither. u = {7, -2} v = {-4, -14}

Assignment Pg