Question

I need help with this math equation

Answer 1

Vector is a quantity that consists of both magnitude and direction. We can represent vectors in various ways such as in matrices form,
`\displaystyle{a\hat i + b\hat j}` or in bracket form
`\displaystyle{\langle a,b \rangle}`.

The magnitude of vector is represented in the form of
`\displaystyle` which equals to
`\displaystyle{√(a^2+b^2)}`.

Substitute components in the formula:

A.
`\displaystyle\langle 5,7 \rangle`

`\displaystyle{√(5^2+7^2)}\\\\\displaystyle{√(25+49)}\\\\\displaystyle{√(74) \approx 8.602}`

B.
`\displaystyle\langle -12, 13 \rangle`

`\displaystyle{√((-12)^2+13^2)}\\\\\displaystyle{√(144+169)}\\\\\displaystyle{√(313)}`

C.
`\displaystyle`

`\displaystyle{√(14^2+(-11)^2)}\\\\\displaystyle{√(196+121)}\\\\\displaystyle{√(317)}`

D.
`\displaystyle\langle -14, -6 \rangle`

`\displaystyle{√((-14)^2+(-6)^2)}\\\\\displaystyle{√(196+36)}\\\\\displaystyle{√(232)}`

Please let me know if you have any questions!