Question

Given the vectors, a=3i+4j, b=-2i+5j, c=10i-j, d=-1/3i+5/2j, find -0.4a-0.3b+0.2d=?

Answer 1

`-(2)/(3)i - (13)/(5)j`

Explanation:

-0.4(3i + 4i) - 0.3(-2i + 5j) + 0.2(-
`(1)/(3)i` +
`(5)/(2)`j)

-1.2i - 1.6j + 0.6i - 1.5j -
`(0.2)/(3)`i + 0.5j

Converting to fraction form;

`-(6)/(5)i + (3)/(5)i - (1)/(15)i - (8)/(5)j - (3)/(2)j + (1)/(2) j`

Solving the i part;

`(-18i + 9i - i)/(15)` =
`-(2)/(3)i`

Solving the j part;

`(-16j-15j+5j)/(10) = -(13)/(5)`j

So -0.4a - o.3b + 0.2d =
`-(2)/(3)i` -
`(13)/(5)j`