# Calculating Vector Product of A and B

• draotic
In summary, the conversation involves a user asking for help with finding the vector product of two given vectors A and B. The expert provides guidance on how to use the distributive law and expand the brackets to solve for the vector product. They also clarify the use of "x" for vector product and "." for scalar product. The user eventually understands and thanks the expert for their help.
draotic

## Homework Statement

Given A= i + j (caps) and B=i+k (caps)..what is the value of vector product of A and B?

## The Attempt at a Solution

....
i tried but can't get this one

Last edited:
welcome to pf!

hi draotic! welcome to pf!

write it (i + j) x (i + k), and use the distributive law

(ie, expand the brackets! ) …

what do you get?

tiny-tim said:
hi draotic! welcome to pf!

write it (i + j) x (i + k), and use the distributive law

(ie, expand the brackets! ) …

what do you get?
thanx
but i still can't get it
opng brackets: i.i +i.k + j.k + j.i
i.i=0
wat now

hi draotic!

(try using the B tag just above the Reply box )
draotic said:
opng brackets: i.i +i.k + j.k + j.i
i.i=0

that's right!

except of course, please use "x" for the vector product (the https://www.physicsforums.com/library.php?do=view_item&itemid=85" ), and "." for the scalar product (the dot product )

i x i = 0

j x i = -i x j = … ?

Last edited by a moderator:
tiny-tim said:
hi draotic!

(try using the B tag just above the Reply box )

that's right!

except of course, please use "x" for the vector product (the https://www.physicsforums.com/library.php?do=view_item&itemid=85" ), and "." for the scalar product (the dot product )

i x i = 0

j x i = -i x j = … ?
can u hlp me to convert this cross product in i j k form?

Last edited by a moderator:
Last edited by a moderator:

## 1. What is the formula for calculating the vector product of A and B?

The formula for calculating the vector product (also known as the cross product) of two vectors A and B is:

A x B = (AyBz - AzBy)i + (AzBx - AxBz)j + (AxBy - AyBx)k

where i, j, and k are the unit vectors in the x, y, and z directions, respectively.

## 2. What is the geometrical interpretation of the vector product?

The vector product of two vectors A and B results in a vector that is perpendicular to both A and B. The magnitude of the vector is equal to the product of the magnitudes of A and B multiplied by the sine of the angle between them. The direction of the vector is given by the right-hand rule, where the thumb points in the direction of the cross product when the fingers of the right hand are curled towards B starting from A.

## 3. Can the vector product of two vectors be commutative?

No, the vector product is not commutative, meaning that A x B is not equal to B x A. The resulting vector will have the same magnitude, but the direction will be opposite.

## 4. How is the vector product related to the dot product?

The vector product and dot product are both operations on vectors, but they result in different quantities. The dot product results in a scalar quantity, while the vector product results in a vector quantity. Additionally, the dot product is commutative, while the vector product is not. The two operations are related through the triple product, where A x (B x C) = (A · C)B - (A · B)C.

## 5. What is the physical significance of the vector product?

The vector product has many physical applications, such as calculating torque in physics or determining the direction of a magnetic field. It is also used in engineering and computer graphics for calculating rotations and orientations. Additionally, the vector product is used in vector calculus to find the curl of a vector field.

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