VCE Specialist 3/4 Question Thread!

[BubbleWrapMan]

That's fine, I do it that way as well, it's usually neater.

[zvezda]

That's fine, I do it that way as well, it's usually neater.

I thought so, i just keep getting the incorrect answer for some reason.
Thanks

And with q2 part ei on last yrs exam 2, wouldnt there need to be some sort of consideration of the range of Arg given that its restricted to -pi to pi inclusive?

[BubbleWrapMan]

No, since it's only asking when the result is imaginary. For instance, is imaginary regardless of whether you restrict its argument.

[Limista]

There is a square based pyramid, with vertices A (0,0,0) and B(14,8,8)  and C (22, 10, -8), and D.

a) find coordinates of point D

b) find coordinates of apex/vertex E, given height of square based pyramid is 45.

Thanks

[BubbleWrapMan]

AD should be equal to BC, I can't see a simple way to do part b without using the cross product though. But, you basically find a vector normal to the square base, scale it so it's of length 45, then add it to AP, where P is the centre of the square base, which should give you AE.

Not a particularly well-phrased question anyway, since there's two possible answers. Where's it from?

[Limista]

how do you find the vector perpendicular to the square base?

It's off a practice SAC given to me by my teacher

[BubbleWrapMan]

Find a, b, c such that ai + bj + ck is perpendicular to both AD and AB (i.e. their dot product is zero), and so you have enough equations, let ai + bj + ck have magnitude 45 (then a^2 + b^2 + c^2 = 45^2). Solve the three equations simultaneously; you should get two different answers, just pick any.

Easier way is to find AB x AD, but that's not on the course.

[Limista]

To find vertex E, what I did was:

Equation1: PA.PE = 0

Equation 2: PD.PE = 0

Equation 3: size of PE = 45

where P is the centre point of square pyramid.

Therefore E= (11,5, -4)

Is this right?

[BubbleWrapMan]

(11, 5, -4) is what I'm getting for P

[Limista]

Okay.

I did what you suggested, and got E(20, -40, 5) and E(-20, 40, -5)?

[BubbleWrapMan]

Those are the possible vectors for PE, so you need to find AP + PE, which will give you the coordinates of E. So, either (-9, 45, -9) or (31, -35, 1).

[aestheticatar]

How's it going guys?
Help would be much appreciated.


Is the following statement true or false? Justify your answer.

        


Thanks in advance! 

[enwiabe]

How's it going guys?
Help would be much appreciated.


Is the following statement true or false? Justify your answer.

        


Thanks in advance! 

A great way of doing this question is to draw a few scenarios of this condition for arbitrary f(x)'s. This will elucidate the answer.

[Limista]

Those are the possible vectors for PE, so you need to find AP + PE, which will give you the coordinates of E. So, either (-9, 45, -9) or (31, -35, 1).

thanks. I'm going to stay with E as being (31, -35, 1). I don't think E will have a negative i value.

[BubbleWrapMan]

No reason it can't though.