What is the length of the vector $-i + 18j - 6k$? - HSC - SSCE Mathematics Extension 2 - Question 1 - 2020 - Paper 1

The length (magnitude) of a vector ( extbf{v} = a\textbf{i} + b\textbf{j} + c\textbf{k} ) is calculated using the formula: $\| \textbf{v} \| = \sqrt{a^2 + b^2 + c^2}$

In this case, the components of the vector are:

• ( a = -1 )
• ( b = 18 )
• ( c = -6 )

Substituting these values into the formula gives:

$\| \textbf{v} \| = \sqrt{(-1)^2 + (18)^2 + (-6)^2}$

Calculating each term, we have:

• ( (-1)^2 = 1 )
• ( (18)^2 = 324 )
• ( (-6)^2 = 36 )

Now adding them together: $1 + 324 + 36 = 361$

Finally, taking the square root: $\| \textbf{v} \| = \sqrt{361} = 19$. Thus, the length of the vector is ( 19 ).