Question

Let A vector=icapAcosu+jcapAsinu is a vector. another vector, B vector is the perpendicular to A vector, then -
1.icapBcosu+jcapBsinu
2.icapBsinu-jcapBcosu

Answer 1

B vector is the perpendicular to A vector, thus,
A∙B=0
1.
(iAcosu+jAsinu )(iBcosu+jBsinu)=AB(cos^2⁡u+sin^2⁡u )=AB≠0
2.
(iAcosu+jAsinu )(iBsinu-jBcosu)=AB(cosusinu-sinucosu)=0
Thus, the second choice is true.
Answer: 2. iBsinu-jBcosu.