Question

The sum of A and B is 5i+j and their difference is 3i-j what is vector A?

Answer 1

`i`

Explanation:

vector `A` can be written as `ai + bj` where `a` and `b` are two unknowns.

vector `B` can be written as `ci + dj` where `c` and `d` are two unknowns.

`(ai + bj) + (ci + dj) = (a+c)i + (b+d)j = 5i + j`

`a+c = 5, b+d = 1`

`(ai + bj) - (ci + dj) = (a-c)i + (b-d)j = 3i - j`

`a-c = 3, b-d = -1`

`a + c = 5, a - c = 3`

`a + c = (a-c) + 8`
`a + c = a - c + 8`
`c = -c + 8`
`2c = 8`
`c = 4`

`a + c = 5`
`a + 4 = 5`
`a = 1`

`b+d = 1, b-d = -1`

`b + d = (b-d) + 2`
`b + d = b - d + 2`
`d = -d + 2`
`2d = 2`
`d = 1`

`b + d = 1`
`b + 1 = 1`
`b = 0`

hence, we have
`a = 1`
`b = 0`

`c = 4`
`d = 1`

vector `A = ai + bj`
substituting the `a` and `b` values in gives `i + 0`, or `i`.

Answer 2

The sum of A and B is 5i+j

• `bbA + bbB = 5 bbi + bb j qquad square`

"and their difference is 3i-j"

• `bbA - bbB = 3 bbi - bb j qquad triangle`

what is vector A?

`square + triangle = 2 bbA = 8 bb i implies bbA = 4 bb i`