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How would you show that a vector is normal to a plane in 3D space?

There are 2 main methods for finding a normal vector. If you know two vectors that lie in the plane e.g. (a,b,c) and (d,e,f), we can find a normal vector by calculating the vector/cross product of (a,b,c) an...
FK
Answered by Fionn K. • Maths tutor
29117 Views

Work out 416 + 49 + 274

739
IM
Answered by Isobel M. • Maths tutor
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Kieran, Jermaine and Chris play football. Kieran has scored 8 more goals than Chris. Jermaine has scored 5 more goals than Kieran. Altogether they have scored 72 goals. How many goals did Jermaine score?

Find an equation that explains the problem. We can see how many goals the players have scored in comparison to each other. The person with the fewest goals is Chris. Let us say he score x goals. Then we can ...
DC
Answered by Daniel C. • Maths tutor
19286 Views

Find the gradient of the exponential curve y(x)=(9e^(7x))/(12e^(2x)) at x=2/5

According to the quotient rule, when y(x)=f(x)/g(x), y'(x)=(f'(x)g(x)-g'(x)f(x))/g(x) 2 f(x)=9e 7x f'(x)=63e 7x , g(x)=12e 2x g'(x)=24e 2x y'(x)=(63e 7x .12e 2x -24e 2x .9e 7x )/(12e 2x ) 2 y'(x)=(756e 9x -2...
CM
Answered by Connor M. • Maths tutor
3606 Views

Use the double angle formulae and the identity cos(A+B)≡cos(A)cos(B)−sin(A)sin(B) to obtain an expression for cos 3x in terms of cos x only

To answer, you need to know and be able to use your trigonometric formulae including the double angle formulae on data sheet. 1: cos(3x)=cos(2x+x) = cos(2x)cos(x) - sin(2x)sin(x) split the 3x into two terms,...
SH
Answered by Sam H. • Maths tutor
19050 Views