A vector, starting at the origin and going to point (-2,0):
Since there is no y-component, the magnitude is the absolute value of the x component
magnitude = 2
magnitude of a vector = sqrt( X2 + Y2) = sqrt ((-2)2 + 02) = sqrt(4) = 2
where X & Y are the x-component & y-component of the vector.
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Divide the vector by it's length (magnitude).
The cosine function is used to determine the x component of the vector. The sine function is used to determine the y component. Consider a vector drawn on an x-y plane with its initial point at (0,0). If L is the magnitude of the vector and theta is the angle from the positive x axis to the vector, then the x component of the vector is L * cos(theta) and the y component is L * sin(theta).
A dot A = A2 do a derivative of both sides derivative (A) dot A + A dot derivative(A) =0 2(derivative (A) dot A)=0 (derivative (A) dot A)=0 A * derivative (A) * cos (theta) =0 => theta =90 A and derivative (A) are perpendicular
p^2 - 2p - 3 = 0 p^2 - 2p = 3 halve the linear term (-2), square it and add it to both sides p^2 - 2p + 1 = 3 + 1 factor left, gather terms right (p - 1)^2 = 4 (p - 1)^2 - 4 = 0 (1,-4) are the vector points of this parabola You can factor to solve for p (p + 1)(P - 3) p = - 1 p = 3
2x2 - 6x + 4 = 0 2(x2 - 3x + 2) = 0 2(x - 1)(x - 2) = 0 x - 1 = 0 and x - 2 = 0 So, x = 1 and x = 2.