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

To find the length (magnitude) of the vector $extbf{v} = - extbf{i} + 18 extbf{j} - 6 extbf{k}$ we use the formula for the magnitude of a vector in three-dimensional space: $| extbf{v}| = ext{sqr} (x^2 + y^2 + z^2)$ where $x$, $y$, and $z$ are the components of the vector.

In our case:

• $x = -1$
• $y = 18$
• $z = -6$

Substituting the values into the formula: $| extbf{v}| = ext{sqr}((-1)^2 + (18)^2 + (-6)^2)$ Calculating each term:

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

Thus: $| extbf{v}| = ext{sqr}(1 + 324 + 36) = ext{sqr}(361)$ Therefore, the length of the vector is: $| extbf{v}| = 19$