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Find the shortest distance between the lines r = (1, 5, 6) + y(-2, -1, 0) and r = (1, 7, -3) + z(2, 0, 4)

Vector joining the two lines = (1, 5, 6) - (1, 7, -3) = (0, -2, 9)Normal vector to the two lines = (-2, -1, 0) x (2, 0, 4) = (-4, 8, 2) = 2(-2, 4, 1)Hence, using the dot product, shortest distance = (0, -...

Answered by Abhinav H. • Further Mathematics tutor

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(x+4)((x^2) - kx - 5) is expanded and simplified. The coefficient of the x^2 term twice the coefficient of the x term. Work out the value of k.

(x + 4) (x² - kx - 5) = x³- kx² - 5x + 4x² - 4kx - 20 = x³ + (4-k)x² + (-5-4k)x - 20.The coefficients are: (4-k) of x² and (-...

Answered by Márk F. • Further Mathematics tutor

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A straight line passes trough the points A(-4;7); B(6;-5); C(8;t). Use an algebraic method to work out the value of t.

We can write the equation of a straight line like y=ax+b, where a and b are constants. If a point is on the line, the equation will be true for the x,y of the point.Now start with point A: 7 = (-4)a + b. ...

Answered by Márk F. • Further Mathematics tutor

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How would you use the Integration Factor method to solve an ordinary first-order linear differential equation?

The word "ordinary" means that there are only two variables, "first-order" means that the highest derivative is the first derivative and "linear" means that the highest power...

Answered by Kelvin C. • Further Mathematics tutor

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Sketch the curve y= ((3x+2)(x-3))/((x-2)(x+1)) and find values of y for which y>=3

Will have asymptotes at x=2 and x=-1, goes from negative to positive going from -1 to 2 and tends to 3 from below for positive x and tends to 3 from above for negative x. Crosses y axis at 3

Answered by Henry B. • Further Mathematics tutor

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