Question

Vector u has initial point P at (0, 0) and terminal point Q at (5, −8). What are the component form and magnitude of u?

Answer 1

The correct answer is the 3rd option.

The component form of a vector is to write in the form (x, y) the x and y component of a vector.

Since the vector starts at (0, 0) and ends at (5, -8) We can rest the start point to the end point to get the components of the vector:

$\begin{gathered} x\text{ component:} \\ 5-0=5 \\ y\text{ component}\colon \\ -8-0=-8 \end{gathered}$

The component for is:

$\langle5,-8\rangle$

The magnitude of a vector is its' module, we calculate it by:

$\mleft\Vert u\mleft\Vert=\sqrt[]{x^2+y^2}\mright?\mright?$

Where x and y are the components of the vector. In this case:

$\mleft\Vert u\mleft\Vert=\sqrt[]{5^2+(-8)^2}=\sqrt[]{25+64}=\sqrt[]{89}\mright?\mright?$

The whole answer is:

$u=\langle5,-8\rangle;\mleft\Vert u\mleft\Vert=\sqrt[]{89}\mright?\mright?$

Which is option 3.