if a=i+2j+3k, b= -i+k , c= j+k and d= -2i+j+k, then d equals

Question

if a=i+2j+3k, b= -i+k , c= j+k and d= -2i+j+k, then d equals..

 

A.a+3b-c

B.-2a+c

C.-3a-b+5c

D.-a+b+3c

E.5a-7b-9c

Answer 1

This problem is equivalent to solving

 

d = xa + yb + zc = x(1 2 3) + y(-1 0 1) + z(0 1 1) = (-2 1 1)

 

x - y + (0)z= -2

2x + (0)y + z = 1

3x + y + z = 1

 

Solve for x, y, and z.  Using Cramer's rule I got

 

x = -1

y = 1

z = 3

 

d = ax + by + cz = -a + b + 3c

 

The correct answer is (D).