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Properties of a Vector

Vector Addition

Two vectors $\vec{a}$ , $\vec{b}$ are shown in the diagram above. Which of the following is the same vector as $\vec{a}+ \vec{b}$ ?

III II I

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by Brilliant Staff

Given the vectors

$\begin{aligned} \vec{a} &=(1, -4),\\ \vec{b} &=(2, 3),\\ \vec{p} &=-\vec{a}+3\vec{b},\\ \vec{q} &=2\vec{a}-5\vec{b}, \end{aligned}$

what is $2\vec{p}-4\vec{q}?$

(42, 118)

(41, 116)

(43, 120)

(44, 121)

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What real values of $x$ and $y$ satisfy the equation $x(1,2)-y(2,3)=(5, 3)?$

x=0, y=-5

x=0, y=-9

x=-9, y=-7

x=-1, y=-4

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by Brilliant Staff

Which of the following is the same vector as $\vec{c}$ in the regular hexagon below?

Details and assumptions

\vec{a}-2\vec{b}

2\vec{a}-\vec{b}

-\vec{a}+\vec{b}

-2\vec{a}+\vec{b}

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by Brilliant Staff

Two vectors $\vec{a}$ , $\vec{b}$ are shown in the diagram above. Which of the following is the same vector as $\vec{a}- \vec{b}$ ?

III I II

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by Brilliant Staff

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