If A = i + j + k and B = -I + -j + -k, then (A-B) will make angle with A?

Indranil · Jul 16th 2018, 12:16 PM

If A = i + j + k and B = -i + -j + -k , then (A-B) will make angle with A? What is the concept behind it, could you please explain with a diagram? (this is the part from scalar and vector)

studiot · Jul 16th 2018, 01:17 PM

I think it's your turn to have a go, right or wrong, before we help you.

Note you learn more from getting it wrong than getting it right.

If you did this in your opening post you would save lots of time and effort.

Hint. Think about what sort of object A, B and (A-B) are.

topsquark · Jul 16th 2018, 02:15 PM

Originally Posted by Indranil

If A = i + j + k and B = -i + -j + -k , then (A-B) will make angle with A? What is the concept behind it, could you please explain with a diagram? (this is the part from scalar and vector)

A hint: How do you find the angle between any two vectors?

-Dan

Indranil · Jul 16th 2018, 06:48 PM

Originally Posted by topsquark

A hint: How do you find the angle between any two vectors?

-Dan

By dot product of two vectors

Indranil · Jul 16th 2018, 06:49 PM

Originally Posted by studiot

I think it's your turn to have a go, right or wrong, before we help you.

Note you learn more from getting it wrong than getting it right.

If you did this in your opening post you would save lots of time and effort.

Hint. Think about what sort of object A, B and (A-B) are.

Would it be unit vectors?

topsquark · Jul 16th 2018, 07:28 PM

Originally Posted by Indranil

By dot product of two vectors

So, what is the vector A - B?

-Dan

Indranil · Jul 16th 2018, 10:32 PM

Originally Posted by topsquark

So, what is the vector A - B?

-Dan

A-B = A + (-B) = ( i + j + k) + (i + j+ k) = 2i + 2j + 2k

HallsofIvy · Jul 17th 2018, 03:54 AM

Good. Notice that, since B= -A, A- B= A- (-A)= 2A. So what is the angle between A and 2A?

topsquark · Jul 17th 2018, 06:41 AM

Originally Posted by HallsofIvy

Good. Notice that, since B= -A, A- B= A- (-A)= 2A. So what is the angle between A and 2A?

Good spot. I hadn't noticed that.

-Dan

studiot · Jul 17th 2018, 07:19 AM

Originally Posted by HallsofIvy

Good. Notice that, since B= -A, A- B= A- (-A)= 2A. So what is the angle between A and 2A?

Indranil
Note that 2 is a scalar. What happens to direction when you multiply (scalar * vector) ?

Note that you asked for diagrams.
I started to think about drawing htese like the last lot but you demonstrated some ability with algebra.

The foregoing discussion shows how much easier algebra is in this 3 dimensional case.

Do you still want diagrams ar can you now draw your own?

One thing you suggested when I asked what A, B and (A-B) are was that they are unit vectors.

Do you still think this or can you see why none of them are unit vectors?