Vectors, lines, dot product
In an orthonormal frame of the plane: vector coordinates, collinearity, norm and distance, equations of a line, direction and normal vectors, parallelism, intersection, dot product, orthogonality and angle.
- 35 cards
- 5 topics
- Free
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Each topic is weighted the way the exam weighs it.
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A few cards from the deck
Vector: what is it?
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An object of the plane defined by a direction, an orientation along it and a length; in a frame, it is written with its two coordinates (x, y).
For A(x_A, y_A) and B(x_B, y_B), the coordinates of AB are (x_B − x_A, y_B − y_A): end minus start, not the other way round.
A(3, −1) and B(1, 4): what are the coordinates of the vector AB?
- (−2, 5)
- (2, −5)
- (−2, 3)
- (4, 3)
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(−2, 5)
End minus start: (1 − 3, 4 − (−1)) = (−2, 5). (2, −5) computes BA, (−2, 3) loses the sign of −1, and (4, 3) adds the coordinates instead of subtracting them.
The vectors u(x, y) and v(x', y') are collinear if and only if … = 0.
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The vectors u(x, y) and v(x', y') are collinear if and only if xy' − x'y = 0.
Do not mix it up with xx' + yy', which tests orthogonality: the minus sign and the crossed coordinates make collinearity.