 Solution

ID: past-exam-of-the-elasticity-and-plasticity-course-of-the-university-of-oxford/2010/2/a/solution

Assume

k \neq = 0

. Dotting the decomposition with

k

gives

A = \frac{a \cdot k}{∣ k ∣ ^{2}} .

Crossing it on the left by

k

and using

B \cdot k = 0

gives

k \times a = ∣ k ∣^{2} B

. Thus

B = \frac{k \times a}{∣ k ∣ ^{2}} .

Indeed

(k \times a) \times k /∣ k ∣^{2} = a - A k

, verifying the decomposition and the imposed transverse condition.

 New to topics? Read the docs here!