99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

Given p =3 i +2 j +4 k , a = i + j b = j + k c = i + k and p =x a +y b +z c , then x, y, z are respectively

Options

A3 2 , 1 2 , 5 2
B1 2 , 3 2 , 5 2
C5 2 , 3 2 , 1 2
D1 2 , 5 2 , 3 2

Correct answer

B. 1 2 , 3 2 , 5 2

Step-by-step solution

aligned & p =x a +y b +z c & 3 i +2 j +4 k =x( i + j )+y( j + k )+z( i + k ) & 3 i +2 j +4 k =(x+z) i +(x+y) j +(y+z) k aligned On comparing both sides the coefficients of i , j , k , we get x+z=3 x+y=2 and y+z=4 (iii) On solving Eqs. (i), (ii) and (iii), we get x= 1 2 , y= 3 2 , z= 5 2

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