Question

1. A long straight copper wire extends through the points (0,0,0) and (1,2,3)7 in R3. (The wire is much longer than the distance between these two points.) The wire is maintained with a positive electrical charge. A cosmic ray ionizes a nearby argon (r1, 2, T3), which produces a free electron. The electron, being atom located at a = negatively charged, flies straight toward the positively charged wire. It crashes into the copper wire at the point Pz. What is the matrix P? Hint: Use the formula for orthogonal projection from least squares solutions: P A(A"A)-1A" =

Answer 1

Sol Given thal the Points A dargsteaight Coppes wie etends thoogh Co,0,0)T and agan ator loate onizes hay neoly A C Coy&nis als - We hove Lind ataic P ? Foom egiver doaan Date we Sankj A CY,3) cV Coo,o) Fsom the above OA o OA + AB oothe iguoe OA AB CV the v to Pes endicus

v &vr) Hence Pjection Prjeckion vTv V VT let 2. x2) Cx3) 2x3) 3x1 Ex 3) x2)

2 VVT + C2x2) VTV VTv Now Substitute 2 2 2 3 6 4 2