Vectors in 3 Dimensions (Edexcel A-Level Mathematics): Flashcards

Magnitude $|a| = \sqrt{x^2 + y^2 + z^2}$

Use the formula: distance = $||A - B||$.

Unit vector = $a / |a|$, where $|a|$ is its magnitude.

Unit vector = $(6/\sqrt{53}, 1/\sqrt{53}, 4/\sqrt{53})$ with $\sqrt{53} = \sqrt{6^2+1^2+4^2}$

They are multiples of each other: $a = k*b$.

Substitute $k$ from one equation into another.

$|\xi| = \sqrt{5\lambda^2 + \mu^2}$

$\lambda^2 + \mu^2 = r^2$, where $r$ is the magnitude.

Values of $\lambda$ are $\pm 2\sqrt{29}$.

$\mu = -6$ when $\lambda = 4$.