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Math Drills
Vectors
Angles between vectors
Practice 1
Vectors
Angles between vectors
1 / 5
Standard
Calculate.
(
1
2
)
⋅
(
3
1
)
∥
(
1
2
)
∥
∥
(
3
1
)
∥
\frac{\begin{pmatrix} 1 \\ 2 \end{pmatrix} \cdot \begin{pmatrix} 3 \\ 1 \end{pmatrix}}{\left\|\begin{pmatrix} 1 \\ 2 \end{pmatrix}\right\|\left\|\begin{pmatrix} 3 \\ 1 \end{pmatrix}\right\|}
(
1
2
)
(
3
1
)
(
1
2
)
⋅
(
3
1
)
1
1
2
\frac{1}{2}
2
1
2
2
2
\frac{\sqrt{2}}{2}
2
2
3
−
2
2
-\frac{\sqrt{2}}{2}
−
2
2
4
3
2
\frac{\sqrt{3}}{2}
2
3
Answer
