Vectors in 2 Dimensions (AQA A-Level Mathematics): Flashcards

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Vector Addition
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Vector addition

Combining vectors to produce a resultant vector

Two quantities that vectors represent

Magnitude and direction

Resultant vector

Combined effect of original vectors

Two methods for vector addition

Geometric (graphical) and algebraic (component)

Geometric method: how to arrange vectors

Place vectors head to tail

Geometric method: where resultant is drawn from/to

From tail of first vector to head of last vector

Algebraic method: formula for RxR_x

Rx=Ax+BxR_x = A_x + B_x

Algebraic method: formula for RyR_y

Ry=Ay+ByR_y = A_y + B_y

Formula for magnitude of resultant R\mathbf{R}

R=Rx2+Ry2|\mathbf{R}| = \sqrt{R_x^2 + R_y^2}

Formula for direction angle θ\theta of resultant

θ=tan1(RyRx)\theta = \tan^{-1}\left(\frac{R_y}{R_x}\right)

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