Calculating the scalar product

[Wiz]

Hi guys,

I have encountered a problem when calculating the scalar product between two vectors to find an unknown. I used the dot product as below:

u=(2 3)-k
v=(4 1)-pk

I have to find p

u.v=(2 3)-k . (4 1)-pk

Now the answer for this question is 2 x 4 + 3 x 1 x -1 x -p = 0 p= -11

But I have no clue how the answer is created, can someone tell me please.

 

[Deleted member 4993]

Hi guys,

I have encountered a problem when calculating the scalar product between two vectors to find an unknown. I used the dot product as below:

u=(2 3)-k
v=(4 1)-pk

I have to find p

u.v=(2 3)-k . (4 1)-pk

Now the answer for this question is 2 x 4 + 3 x 1 x -1 x -p = 0 p= -11

But I have no clue how the answer is created, can someone tell me please.

Do you know the definition of scalar product and method to calculate the scalar product of vectors?

If not look-up in Google or your textbook.

 

[Wiz]

Do you know the definition of scalar product and method to calculate the scalar product of vectors?

If not look-up in Google or your textbook.

I understand it perfectly, dot product can be used to find the scalar product between two vectors. However what I meant is if

u= 2i + 3j - k
and
v= 4i + j - pk

given that u is perpendicular to v (so their dot product will be 0), how can I find the value of p?

 

[ksdhart]

Well, I'm assuming that k is a vector, and p is a scalar. If these assumptions are not correct, please let me know. If they are, then we'll proceed:

$\displaystyle k=ai+bj$

$\displaystyle u=\left(2-a\right)i+\left(3-b\right)j$

$\displaystyle v=\left(4-pa\right)i+\left(1-pb\right)j$

$\displaystyle u\cdot v=\left[\left(2-a\right)i+\left(3-b\right)j\right]\cdot \left[\left(4-pa\right)i+\left(1-pb\right)j\right]$

Now when I did the dot product, the best I could do was solve for p in terms of a, b, and k. So unless you know more about the problem that you haven't posted, I don't think this is solvable.

 

[Deleted member 4993]

I understand it perfectly, dot product can be used to find the scalar product between two vectors. However what I meant is if

u= 2i + 3j - k
and
v= 4i + j - pk

given that u is perpendicular to v (so their dot product will be 0), how can I find the value of p?

Do you know that:

$\displaystyle i \cdot i = 1$ ......... and

$\displaystyle i \cdot j = 0$ and so forth

Use distributive property of multiplication along properties of dot product.