a dot b x c in vectors?

Question

is there an order of operations? im quessin that i would have to do a dot (b x c)? and can u do a scalar x vector?

Answer 1

Let a , b and c be vectors
a . b X c
If you did a . b first you would obtain a scalar, d say.
You would then have scalar d X c ie the cross product of a scalar and a vector (Can`t be done)
Must therefore have a. (b X c)
(b X c) is a vector d,say
Then have a . d which is permissable (the dot product of two vectors).

For the second question, you can multiply a vector by a scalar but cannot take cross product of scalar times vector.

Answer 2

It only makes sense that it's a dot (b x c) because dot requires two vectors and produces a scaler whereas the cross product takes two vectors and produces a vector.. You cannot dot a vector and a scalar. You can multiply a vector by a scaler but that is a different operation.

Answer 3

As far as I know, you cannot cross a scalar with a vector. In fact, you cannot perform either operation unless both values are vectors. Since they must both be vectors, it would a b X c first; that would result in a new vector, then dot A with the new vector.

Answer 4

merely brute rigidity it: a = b = c = b x c = a dot (b x c) = ax by making use of cz - ax bx cy + ay bz cx - ay bx cz + az bx cy - az cx and then do the different edge the comparable way and instruct it is equivalent. no longer something stressful, merely sort of tedious protecting music of each and every of the words. There are honestly greater stylish tips on a thank you to instruct that the triple product is cyclic, yet i think of they only choose you to easily turn the crank right here.