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How can you find out if two lines expressed in their vector form intersect?

Let the lines be: r 1 = (a, b, c) + t(d, e, f) r 2 = (g, h, i) + s(j, k, l) Since t and s above are variables and the rest of the letters are constants, the only way to change the point which the vector equa...
YI
Answered by Yordan I. • Maths tutor
4838 Views

How to get started on an essay?

Writing an essay - whether it's for coursework submission or practice for an exam - can seem really really overwhelming sometimes. It's not as hard as it seems, if you know where to start though! First, you ...
LG
Answered by Lili G. • English tutor
2727 Views

How does an increase in the interest rate affect the level of investment?

The key to answering this question is understanding that interest rates determine the cost of borrowing. If you borrow £1000 to buy a car at 10% annualised interest rate, your cost of borrowing would be less...
JG
Answered by James G. • Economics tutor
5161 Views

How to Integrate ln(x)?

Integrating this expression is a simple trick. We use integration by parts. For this we need a function we can integrate and a function we can differentiate. We know how to differentiate ln(x) which is 1/x. ...
JR
Answered by Jordan R. • Maths tutor
7719 Views

What is entropy?

Entropy is the level of disorder in the universe. The more disordered something is, the higher its entropy. Molecules in solids ae specifically arranged and vibrating, hence the level of disorder is low, mea...
RB
Answered by Rajas B. • Chemistry tutor
2708 Views