How to find a vector given the scalar triple productScalar triple product formula: a (...

anudoneddbv

anudoneddbv

Answered

2022-07-20

How to find a vector given the scalar triple product
Scalar triple product formula: a ( b × c )
If I know the value of the product and I know what vectors b and c are, how do I find what vector a is equal to?

Answer & Explanation

ri1men4dp

ri1men4dp

Expert

2022-07-21Added 14 answers

Unfortunately, you can't. Your real question is even simpler: if you know x and a x = y, can you solve for a?
The issue is that the dot product is not an invertible operation, so there are lots of ways to choose x such that a x = y. Think about it for the two-dimensional cases: let a = [ a 1 , a 2 ] and x = [ x 1 , x 2 ]. The hypothesis is that we know x 1 , x 2 , y, and that
a 1 x 1 + a 2 x 2 = y ,
but this is a single equation with two unknowns ( a 1 and a 2 ), which has infinitely many solutions. If that seems odd, verify that a = [ 0 , y x 2 ] and a = [ y x 1 , 0 ] are both solutions

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?