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MATH / When begin{pmatrix} a b end{pmatrix} is projected onto begin{pmatrix} sqrt{3} 1 end{pmatrix}, the resulting vector has magnitude √(3). Also, a=2+b√(3). Enter all possible values …

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problem

When $\begin{pmatrix} a \\ b \end{pmatrix}$ is projected onto $\begin{pmatrix} \sqrt{3} \\ 1 \end{pmatrix},$ the resulting vector has magnitude 3.\sqrt{3}. Also, a=2+b3.a = 2 + b \sqrt{3}. Enter all possible values of a,a, separated by commas.
Plain-text mathematical notation (without MathML)
When $\begin{pmatrix} a \\ b \end{pmatrix}$ is projected onto $\begin{pmatrix} \sqrt{3} \\ 1 \end{pmatrix},$ the resulting vector has magnitude √(3).  Also, a=2+b√(3).  Enter all possible values of a, separated by commas.
Original LaTeX notation
When $\begin{pmatrix} a \\ b \end{pmatrix}$ is projected onto $\begin{pmatrix} \sqrt{3} \\ 1 \end{pmatrix},$ the resulting vector has magnitude $\sqrt{3}.$  Also, $a = 2 + b \sqrt{3}.$  Enter all possible values of $a,$ separated by commas.

level

Level 5

type

Precalculus

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Source and history

task_id
3b5c8e51-2d73-5bb9-aa32-1661815918d6
task_key
precalculus--test--3b5c8e51-2d73-5bb9-aa32-1661815918d6
task_revision_id
1
config / split
precalculus / test

Official source

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