Distance of this vector?

Question

using the formulae d = |OA.OB|

where OA=[1,2,3]
OB=1/6[4,-4,-2]

there are many formulaes i found and im confused, is the answer -5/3(from doing 1X2+2X-4+3X-2...but thats the vector product)??
please show the working ,

Answer 1

sorry, but i think your vector is either written wrong or this is a matrix or it is neither, because vectors can only have 2 digits!if this is a matrix, then the two lines on either side of 'OA. OB' mean that you should find the determinant. the formula for this is: 1/determinant*(d -b)
(-c a)
notice that the elements, d and a, of the real have been changged, and the signs of, b and c, changed ( this is a 2 by 2 matrix with d ontop of -c and -b ontop of a)

Answer 2

The formula you posted is the absolute value of the dot product. It is NOT the same as the vector product.

First let's simplify OB.

OB = (1/6)<4, -4, -2> = <4/6, -4/6, -2/6>
OB = <2/3, -2/3, -1/3>

Now let's take the absolute value of the dot product.

|OA • OB| = <1, 2, 3> • <2/3, -2/3, -1/3>

|OA • OB| = |1*(2/3) + 2*(-2/3) - 3*(-1/3)|

|OA • OB| = |2/3 - 4/3 - 1| = 5/3