Question

Three vectors a, b, and c are related to one another such that 2a + 3b = 18c. A fourth vector d exists such that 6c + d =

a. Determine an expression for d in terms of the vectors a and
b.

Answer 1

we are given equations of vectors as

`2a + 3b = 18c`

`6c + d = a`

now, we want to find an expression for d in terms of the vectors a and b

so, we can eliminate c from second equation

so, we will solve for c from first equation

`2a + 3b = 18c`

divide both sides by 18

we get

`c=(1)/(9) a+(1)/(6) b`

now, we can plug this in second equation

`6((1)/(9) a+(1)/(6) b) + d = a`

we can simplify it

`6*(1)/(9) a+6*(1)/(6) b + d = a`

`(2)/(3) a+ b + d = a`

`d = a-(2)/(3) a-b`

`d = (1)/(3) a-b`..............Answer