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How do I find the dot product of two 3-dimensional vectors

Example; Let vector v = (2,5,2) and vector u = (1,-2,3),then u · v = [(2 x 1) + (5 x -2) + (2 x 3)] = [2 -10 + 6] = -2 As the workings hopefully make clear in the line above, the general formula for the scal...
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Answered by Theo V. • Maths tutor
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Sketch the graph of y= (x^2) -2x -3 labelling the turning points and points of intersection

The gradient of the curve equals the first derivative.dy/dx = 2x - 2At the turning point the gradient equals zero.2x -2 = 02x = 2 x= 1to find the y co-ordinate to this point substitute x = 1 into the origina...
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Answered by Lavana C. • Maths tutor
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Multiple choice. If the sequence is 9, 16, 25, 36, 49 choose the correct expression. A. n^2 B. (3n)^2 C. (n+2)^2

Fist draw a table of the sequence with each number's corresponding n value.1 2 3 4 5 9 16 25 36 49Now draw a table for each option and see if it matches, it is important to remember to carry out the sum with...
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Answered by Lavana C. • Maths tutor
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Find the an expression for dy/dx of the function y=(4x+1)ln(3x+1) and the gradient at the point x=1.

This question is example of product rule. To simplify need to define two terms u=4x+1 and v=ln(3x+1). Each term is then differentiated. du/dx=4. To differentiate v, need to define another term a=3x+1, theref...
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Answered by William S. • Maths tutor
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A curve has the equation x^2 +2x(y)^2 + y =4 . Find the expression dy/dx in terms of x and y [6]

Integrate each term in terms of x, then integrate each term in terms of y Make sure you state in what form you are integrating. Remember if you are integration in terms of y, the x values are constants and v...
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Answered by Lavana C. • Maths tutor
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