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Multiple Choice
True or false: If a⃗=⟨3,−2⟩ and b⃗ has initial point (−10,5) & terminal point (−7,3), then a⃗=b⃗.
A
True
B
False
C
Cannot be determined with the given information
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Verified step by step guidance
1
First, understand that two vectors are equal if they have the same magnitude and direction. This means their components must be identical.
Given vector a⃗ = ⟨3, -2⟩, we need to find the components of vector b⃗.
To find the components of vector b⃗, use the formula for a vector given its initial point (x1, y1) and terminal point (x2, y2): b⃗ = ⟨x2 - x1, y2 - y1⟩.
Substitute the given points for b⃗: initial point (-10, 5) and terminal point (-7, 3). Calculate the components: b⃗ = ⟨-7 - (-10), 3 - 5⟩.
Simplify the components of b⃗: b⃗ = ⟨3, -2⟩. Now compare the components of a⃗ and b⃗. Since they are identical, a⃗ = b⃗, so the statement is True.