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

[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)

 

[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.

 

[topsquark]

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]

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

-Dan

By dot product of two vectors

 

[Indranil]

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]

By dot product of two vectors

So, what is the vector A - B?

-Dan

 

[Indranil]

So, what is the vector A - B?

-Dan

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

 

[HallsofIvy]

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

 

[topsquark]

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]

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?