Math Problem Statement
Om vektorerne
"#mover(mi("a"),mo("→"))
"
og
"#mover(mi("b"),mo("→"))
"
oplyses
"abs(#mover(mi("a"),mo("→"))
) = 7"
,
"abs(#mover(mi("b"),mo("→"))
) = 9"
og "v((a),(b))=13°"
.
Skitsér situationen, og beregn
"#mover(mi("a"),mo("→"))
*#mover(mi("b"),mo("→"))
"
.
Vektorerne
"#mover(mi("c"),mo("→"))
"
og
"#mover(mi("d"),mo("→"))
"
er givet ved koordinaterne
"#mover(mi("c"),mo("→"))
= <20, 30>"
og
"#mover(mi("\
d__k`"),mo("→"))` = <50, k>"
.
Skitsér situationen, og bestem "k"
så "v((c),((d))[k])=70°"
.
Solution
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Math Problem Analysis
Mathematical Concepts
Vector Magnitude
Dot Product
Angle Between Vectors
Formulas
Dot Product Formula: a ⋅ b = |a| |b| cos(θ)
Vector Magnitude Formula: |v| = sqrt(x^2 + y^2)
Dot Product Formula (Component Form): a ⋅ b = x1*x2 + y1*y2
Theorems
Dot Product Theorem
Suitable Grade Level
Grades 11-12
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