AP EAMCET20225 Jul 2022Morning ShiftMathematicsVector AlgebraActual

a , b , c are non-coplanar vectors. If aligned & a +3 b +4 c =x( a -2 b +3 c )+y( a +5 b -2 c ) & +z(6 a +14 b +4 c ), then x+y+z= aligned

Options

Correct answer

B. -4

Step-by-step solution

a +3 b +4 c = a (x+y+6 z)+ b (-2 x+5 y+14 z)+c(3 x-2 y+4 z) (because a, b and c are non-coplanar vectors) Comparing both sides, x+y+6 z=1 ...(i) -2 x+5 y+14 z=3 ...(ii) 3 x-2 y+4 z=4 ...(iii) By solving Eqs. (i), (ii) and (iii), we get aligned & x=-2, y=-3, z=1 & x+y+z=-4 aligned

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