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# core 4 queries? Watch

1. 7) A curve has parametric equations

x = e^2t, y =2t/(1 + t)

(i) Find the gradient of the curve at the point where t = 0
(ii) Find y in terms of x.

9) The points A, B and C have coordinates (1, 3, ?2), (?1, 2, ?3) and (0, ?8, 1) respectively.
(i) Find the vectors AB and AC.
(ii) Show that the vector 2i ? j ? 3k is perpendicular to the plane ABC. Hence find the equation of
the plane ABC.

I tried to do nine by doing the dot product, but i couldnt get it to work?

Anyone give me a clue please?
2. (Original post by fujitsum)
7) A curve has parametric equations

x = e^2t, y =2t/(1 + t)

(i) Find the gradient of the curve at the point where t = 0
(ii) Find y in terms of x.

9) The points A, B and C have coordinates (1, 3, ?2), (?1, 2, ?3) and (0, ?8, 1) respectively.
(i) Find the vectors AB and AC.
(ii) Show that the vector 2i ? j ? 3k is perpendicular to the plane ABC. Hence find the equation of
the plane ABC.

I tried to do nine by doing the dot product, but i couldnt get it to work?

Anyone give me a clue please?
What about question 7, you stuck on both bits?
3. Yep!
4. for question 7, show your working
5. (Original post by fujitsum)
Yep!
7)

i) The gradient of a parametric curve would be dy/dt * dt/dx. (Can you find dt/dx?)

ii) You need to find a way of writing this as a cartesian equation, so you'll need to get rid of the t.

9) I assume the question marks are minus signs.
6. What are the ? meant to be?
7. (Original post by fujitsum)
9) The points A, B and C have coordinates (1, 3, ?2), (?1, 2, ?3) and (0, ?8, 1) respectively.
(i) Find the vectors AB and AC.
(ii) Show that the vector 2i ? j ? 3k is perpendicular to the plane ABC. Hence find the equation of
the plane ABC.

I tried to do nine by doing the dot product, but i couldnt get it to work?

Anyone give me a clue please?
Assuming you're asking for a clue with part (ii), you're using a.b = |a||b|cos(x), right?

If the plane and the vector are perpendicular, what's the angle between them? How does that affect the RHS?
8. Yeah, the question marks are minus signs, don't know why its done that.

I am really clueless?? I don't get how to differentiate anything on q7.
9. (Original post by fujitsum)
Yeah, the question marks are minus signs, don't know why its done that.

I am really clueless?? I don't get how to differentiate anything on q7.

You'll want to find the derivitive of y with respect to t, and the derivitive of t with respect to x. (This is the same as the reciprocal of the derivitive of x with respect to t).

Do you know how to differentiate e^x and quotients?
10. (Original post by EEngWillow)
If the plane and the vector are perpendicular, what's the angle between them? How does that affect the RHS?
I dooon't know??
11. (Original post by EEngWillow)

You'll want to find the derivitive of y with respect to t, and the derivitive of t with respect to x. (This is the same as the reciprocal of the derivitive of x with respect to t).

Do you know how to differentiate e^x and quotients?
Nope, well, i might recognise it, but i don't have any of the assumed knowledge from core 3!
12. (Original post by fujitsum)
Nope, well, i might recognise it, but i don't have any of the assumed knowledge from core 3!
Just realised I ****ed up my LaTeX completely, equation is fixed now.

When you differentiate e^5x, you'll get 5e^5x. You have e^2t, so you'll get?

The quotient rule is dy/dx = (vdu - udv)/v^2, where u is the numerator and v the denominator. You use it when you have a fraction where both the numerator and denominator are functions of the variable you're differentiating with respect to.

And for question 9: When two lines are perpendicular, the angle between them is 90 degrees. cos(90) = 0, so if they're perpendicular your scalar product will equal 0.
13. 2e^2t then!

I'll revise quotient rule and have a crack at it then!

How do you do the dot product correctly?

I x'd the two vectors (A&B) together? That doesnt = 0 though?

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