Question

If `bar("AB") = 2hat"i" + hat"j" - 3hat"k"`, and A(1, 2 ,−1) is given point then coordinates of B are ______.

Options

• (3, 3, −4)

• (−3, 3 −2)

• (3, 3, 2)

• (−3, 3, 4)

Answer 1

If `bar("AB") = 2hat"i" + hat"j" - 3hat"k"`, and A(1, 2 ,−1) is given point then coordinates of B are (3, 3, −4).

Explanation:

Given:

`bar("AB") = 2hat"i" + hat"j" - 3hat"k"`

A(1, 2 ,−1)

To find:

B(x, y, z)

`vec(AB) = vecB - vecA`

`vecB = vecA + vec(AB)`

`vecA = 1hati + 2hatj - hatk`

`vec(AB) = 2hati + hatj + -3hatk`

Adding `vecA` and `vec(AB)`

`vecB = (1hati + 2hatj - hatk) + (2hati + hatj - 3hatk)`.

∴ `vecB = (1 + 2)hati + (2 + 1)hatj + (-1 -3)hatk`

∴ `vecB = 3hati + 3hatj -4hatk`

∴ The coordinates of B are (3, 3, −4).