7.8 Prove, by writing it out in component form, that (a × b) × c = (ac)b — (b. c)a, and deduce the result, stated in equation (7.25), that the operation of forming the vector product is non-associative.

Q: Find a vector b such that |b| = 1/2 that is parallel to a = but with opposite direction.

A: Given that: |b|=12a=<-6, 3, -2>

Q: Express the vector below in Cartesian coordinate: B = 2r sin cosc a₁ + r cose cose aer sind a ax=…

A: Given: The vector, B=2rsinθcosφar+rcosθcosφaθ-rsinφaφ   To express: The given vector in cartesian…

Q: Given that (A x B) x (C x D) = [A,C,D]B - [B,C,D]A, derive (A x B) x (C x D) = [A,B,D]C - [A,B,C]D…

A: To derive the second identity , assuming the truth of the first

Q: Find the vector proj, u. v = 3i - j+ 3k, u = 2i + 10j + 11k %3D 0,一+店x k 19 i+ 22 15 19 19

A: Given : v = 3i - j + 3k, u = 2i + 10j + 11k   To find the vector projv u.

Q: Express the vector v =12i -5j as the sum of a vector parallel to b = 3i +4j and a vector orthogonal…

A: here we have to write the vector v in the form: v→=β1+β2Where β1 is parallel to b→ and β2 is…

Q: (2.) Let V be the vector space of M1x2(C) over R. (a.) Give a basis for V. (b.) Let W = { { 1] z €R.…

A:

Q: Find a vector v such that ||v||=5, and v is in the opposite direction of -5i+7j .

A: We have a vector -5i+7j Let u→=-5i+7j First, we find a unit vector in the direction of u→=-5i+7j The…