• Math Archive: Questions from 2024-09-2

    Name all the equal vectors in the parallelogram shown. (i) AB→ is equal to what? EB→ CB→ DC→ CE→ DA→ is equal to what? DC→ CB→ EB→ CE→ DE→ is equal to what? DC→ EB→ CE→ CB→ EA→ is equal to what? DC→ CB→ EB→ CE→
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    Using the vectors shown in the figure, write each sum or difference as a single vector. (a) AB→ + BC→ (b) CD→ + DB→ (c) DB→ − AB→ (d) DC→ + CA→ + AB→
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    In the figure, the tip of c and the tail of d are both the midpoint of QR. Express c and d in terms of a and b. c = d =
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    Find a vector a with representation given by the directed line segment AB→. A(−4, 2), B(2, 4) Draw AB→ and the equivalent representation starting at the origin.
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    Find a vector a with representation given by the directed line segment AB→. A(−5, −3), B(2, 5) Draw AB→ and the equivalent representation starting at the origin.
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    Find the sum of the given vectors. a = ⟨3, −3⟩, b = ⟨−2, 8⟩ Illustrate geometrically.
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    Find a+b, 6a + 9b, |a|, and |a − b|. (Simplify your vectors completely.) a = ⟨−5, 12⟩, b = ⟨10, 4⟩ a + b = 6a + 9b = |a| = |a − b| =
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    Find a unit vector that has the same direction as the given vector. −7i + 3j − k
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    Find the vector that has the same direction as ⟨3, 6, −2⟩ but has length 2.
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    What is the angle between the given vector and the positive direction of the x-axis? (Round your answer to the nearest degree.) 20i + 15j
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    If A, B, and C are the vertices of a triangle, find AB→ + BC→ + CA→. CB→ AC→ 0 BA→
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