- #1

- 48

- 5

- Homework Statement
- Let B = (v⃗1, v⃗2, v⃗3) be any basis of R3 consisting of perpendicular unit vectors, such that v⃗3 = v⃗1 × v⃗2. Let T(x⃗) = v⃗1 × x⃗ + (v⃗1 · x⃗)v⃗1. Find the B-matrix B of the given linear transformation T from R3 to R3. Interpret T geometrically.

- Relevant Equations
- dot product

cross product

Could anyone explain the reasoning from step 2 to step 3?

Specifically, I don't understand how to find the product of a cross product and a vector - like (v1 · v2)v1 and (v1 · v3)v1. I'm also confused by v1 × v3 + (v1 · v3)v1 -- is v1 × v3 = v1v3? How would this be added to (v1 · v3)v1?

Thank you.