The vector b= 3j + 4k is to be written as the sum of a vector u parallel to A= i +j and a vector v perpendicular to A. Then find value of u.

Asked by sunil2791 | 17th Nov, 2017, 07:05: PM

Expert Answer:

begin mathsize 16px style space straight b equals space 3 straight j space plus space 4 straight k
straight b equals straight u plus straight v..... left parenthesis 1 right parenthesis
straight u equals straight lambda open parentheses straight i plus straight j close parentheses..... parallel
straight A. straight v equals 0...... perpendicular
open parentheses straight i plus straight j close parentheses. open parentheses xi plus yj plus zk close parentheses equals 0
straight x equals negative straight y
so space straight v equals xi minus xj plus zk
from space left parenthesis 1 right parenthesis
3 straight j space plus space 4 straight k equals open parentheses λi plus λj close parentheses plus open parentheses xi minus xj plus zk close parentheses
so space compare
straight lambda equals 3 over 2
straight u equals 3 over 2 open parentheses straight i plus straight j close parentheses
end style

Answered by Arun | 5th Dec, 2017, 03:58: PM