- #1
draotic
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Homework Statement
Given A= i + j (caps) and B=i+k (caps)..what is the value of vector product of A and B?
Homework Equations
The Attempt at a Solution
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i tried but can't get this one
Last edited:
thanxtiny-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?
draotic said:opng brackets: i.i +i.k + j.k + j.i
i.i=0
can u hlp me to convert this cross product in i j k form?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 = … ?
means the correct anser is i-j-ktiny-tim said:i don't understand what you mean by " https://www.physicsforums.com/library.php?do=view_item&itemid=85" in i j k form"
oops!tiny-tim said:i don't understand what you mean by " https://www.physicsforums.com/library.php?do=view_item&itemid=85" in i j k form"
draotic said:means the correct anser is i-j-k
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.
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.
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.
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.
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.