Question

Given P = (3,-4) and Q= (-2, -4) . Sketch PQ. Find the component form, magnitude, and direction of the vector.

Answer 1

Follows are the solution to this question:

Explanation:

Given:

`P= (3,-4)\\\\Q=(-2,-4)\\\\\overrightarrow{PQ}=?\\\\Magnitude=?\\\\\text{Direction of the vector}=?\\\\`

Calculating
`\overrightarrow{PQ}`:

`\to \overrightarrow{PQ} = \overrightarrow{Q} -\overrightarrow{P}`

`= (-2, -4) - (3,-4)\\\\= (-2\ -3, -4 \ -(-4)) \\\\= (-5 ,0)\\\\ = -5i+0j`

Calculating magnitude:

`\to || \overrightarrow{PQ} || = √(i^2+j^2)`

`=√(-5^2+0^2)\\\\=√(25+0)\\\\=√(25)\\\\=5`

Calculating the direction of the vector:

`\overrightarrow{V} = \frac{\overrightarrow{PQ}}{|| \overrightarrow{PQ}||}`

`= (5i+0j)/(5)\\\\= (5i)/(5)\\\\= i`