MHT CET20226 Aug 2022Evening ShiftMathematicsVector AlgebraActual
a = i + j + k , and b = i - j + k and c = i - j - k are three vectors then vector r in the plane of a and b , whose projection on c is 1 3 , is given by
Options
- A(2 i -1) i - j +(2 t +1) k , t R
- B(2 t +1) i - j +(2 t +1) k , t R
- C(2 t-1) i - j +(2 t-1) k , t R
- D(2 t+1) i - j +(2 t-1) k , t R
Correct answer
B. (2 t +1) i - j +(2 t +1) k , t R
Step-by-step solution
r =t a +u b [as vector lies in the plane of a and b where t and u are scalars] aligned & r =t( i + j + k )+u( i - j + k ) & =(t+u) i +(t-u) j +(t+u) k (i) & r c | c | = 1 3 (t+u)-(t-u)-(t+u) 3 = 1 3 & -(t-u)=1 u=t+1 . .(i i) aligned from (i) and (ii) r =(2 t+1) i - j +(2 t+1) k