Homework Help

Let v1 = a1i + b1j + c1k; v2 = a2i + b2j + c2k; v3 = a3i + b3j + c3k. Find the...

user profile pic

vanillacream | Student | eNotes Newbie

Posted July 27, 2011 at 7:40 PM via web

dislike 0 like

Let v1 = a1i + b1j + c1k; v2 = a2i + b2j + c2k; v3 = a3i + b3j + c3k. Find the solution for v1∙(v2xv3).

1 Answer | Add Yours

user profile pic

giorgiana1976 | College Teacher | Valedictorian

Posted July 27, 2011 at 7:49 PM (Answer #1)

dislike 0 like

We'll recall the result of cross product of two vectors:

v4 = v2xv3 = (b2*c3 - b3*c2)i + (a2*c3 - c2*a3)j + (a2*b3 - b2*a3)k

Now, we'll calculate the dot product of v1*v4:

v1*v4 = a1*(b2*c3 - b3*c2) + b1*(a2*c3 - c2*a3) + c1*(a2*b3 - b2*a3)

The requested solution for v1*(v2xv3) is:

v1*(v2xv3) = a1*(b2*c3 - b3*c2) + b1*(a2*c3 - c2*a3) + c1*(a2*b3 - b2*a3)

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes