# Let vectors A=(1,0,-3) ,B=(-2,5,1) and C=(3,1,1), how do you calculate 2A-3(B-C)?

Feb 1, 2016

( 17 ,-12 , -6 )

#### Explanation:

When adding/subtracting vectors , the x ,y and z components

of a vector are added/subtracted to the x , y and z components
of the other vector.

example: A=(a,b,c) and B=(d,e,f)

then A+B = (a+d,b+e,c+f) . Similarly when subtracting.

components of a vector may also be multiplied by a scalar
using the 'distributive law'.

example: A = ( x,y,z) then 2A = 2(x,y,z) =(2x,2y,2z)

starting with B - C = (-2,5,1) - (3,1,1) = (-5,4,0)

then -3 (B- C) = -3(-5,4,0) = (15,-12,0)

and 2A = 2(1,0,-3) = (2,0,-6)

hence 2A-3(B-C) = (2,0,-6) + (15,-12,0) = (17,-12,-6)