PERPENDICULAR LINES IN SPACE

Let us look at the following scenario.

P is a point and L is a line in space.
If we draw a perpendicular from P to L, will it always intersect L ?

What do you think is the answer?

For the answer click here
---------------------------------------------------------------------------------------------------
 If you need online assistance in mathematics (CBSE, IGCSE, PLUS 1 & 2 ETC.) please contact me on raghavanckk@gmail.com    Skype ID: raghavanckk   Mobile: +27(0)737455575

I charge US$5-10 per hour depending on the topic/class.

I have more than 30 years of experience in teaching mathematics at O and A levels in different countries.  At the moment I am also involved with a Mathematics Development Project under  Rhodes University to improve the mathematics efficiency of High School students in South Africa.

I am conversant with the mathematics curricula of many countries.

LINES IN SPACE : AN INTERESTING QUESTION

We are familiar with geometry in two dimensions and  have plotted points and drawn lines, curves and figures on a piece of paper.

A plane piece of paper presents  a two-dimensional environment. That means only objects having no thickness can be created on a plane piece of paper. But wait! Artists have drawn mountains, brooks and horses on paper. And they are not flat objects. True. They use different intensities of shades and the techniques of perspectives to create the illusion of thickness on a flat surface.

In reality we live in a three -dimensional world. A natural progression therefore is to enquire about what happens in a world of three dimensions.

We talk about space.

Just as we plot points, lines and figures on a plane, we can have points, lines and figures in space.

Let us talk about lines in space.

Statement: Two non-intersecting lines in space are always parallel.

What do you think about this statement?

Please click  here  for the answer

----------------------------------------------------------------------------------------------------------

 If you need online assistance in mathematics (CBSE, IGCSE, PLUS 1 & 2 ETC.) please contact me on raghavanckk@gmail.com    Skype ID: raghavanckk   Mobile: +27(0)737455575

I charge US$5-10 per hour depending on the topic/class.

I have more than 30 years of experience in teaching mathematics at O and A levels in different countries.  At the moment I am also involved with a Mathematics Development Project under  Rhodes University to improve the mathematics efficiency of High School students in South Africa.

I am conversant with the mathematics curricula of many countries.

DIVISIBILITY BY 7 OF A LARGER NUMBER

I hope you have gone through my last post on "A TRICK TO CHECK DIVISIBILITY BY 7".

If the number is large like 6013 or 564743 having more than three digits, then the method is to apply the trick repeatedly.

Let us check if 6013 is divisible by 7.

• Last digit=3
• Double it; we get 6
• Subtract 6 from 601, the answer is 595
• Is 595 divisible by 7? It is rather difficult to answer.
• So, take the lat digit of 595; that is 5
• Double it; we get 10
• Subtract 10 from 59; the answer is 49
• Is 49 divisible by 7?  Yes!
• So, 595 is divisible by 7 and consequently 6013 is divisible by 7.

GOT IT?

----------------------------------------------------------------------------------------------------------

 If you need online assistance in mathematics (CBSE, IGCSE, PLUS 1 & 2 ETC.) please contact me on raghavanckk@gmail.com    Skype ID: raghavanckk   Mobile: +27(0)737455575

I charge US$5-10 per hour depending on the topic/class.

I have more than 30 years of experience in teaching mathematics at O and A levels in different countries.  At the moment I am also involved with a Mathematics Development Project under  Rhodes University to improve the mathematics efficiency of High School students in South Africa.

I am conversant with the mathematics curricula of many countries.

A TRICK TO CHECK DIVISIBILITY BY 7

There are many tricks in mathematics to solve a problem quickly and easily!

Question:  Can you divide 406 by 7 without leaving a remainder?

This is the trick

• Take the last digit of the number
• Double it
• Subtract the number thus obtained from the given number without the last digit
• If you can divide the number obtained by 7, you can divide the given number also by 7

Here, the given number is 406

• Take the last digit. It is 6
• Double it; we get 12
• Subtract 12 from 40; we get 28
• 28 is divisible by 7. So 406 is also divisible by 7.

Now try the following questions.

Which of the following numbers are divisible by 7?
 (a)  441      (b) 623    (c) 474    (d) 4886    (e)  6249      (f)  444724  (g) 75328

Wait for the next post to be published soon to learn about the trick to check divisibility by 7 of a number having 4 or more digits.
----------------------------------------------------------------------------------------------------------

 If you need online assistance in mathematics (CBSE, IGCSE, PLUS 1 & 2 ETC.) please contact me on raghavanckk@gmail.com    Skype ID: raghavanckk   Mobile: +27(0)737455575

I charge US$5-10 per hour depending on the topic/class.

I have more than 30 years of experience in teaching mathematics at O and A levels in different countries.  At the moment I am also involved with a Mathematics Development Project under  Rhodes University to improve the mathematics efficiency of High School students in South Africa.

I am conversant with the mathematics curricula of many countries.