Question

Find the cross product →A × →C for (a) A = 2.0 ^i − 4.0 ^j + ^k and C = 3.0 ^i + 4.0 ^j + 10.0 ^k (b) A = 3.0 ^i + 4.0 ^j + 10.0 ^k and →C = 2.0 ^i − 4.0 ^j + ^k (c) A = −3.0 ^i − 4.0 ^j and →C = −3.0 ^i + 4.0 ^j (d ) →C = −2.0 ^i + 3.0 ^j + 2.0 ^k and A = −9.0 ^j

Answer 1

Recall the rules for the cross product:

i x i = j x j = k x k = 0

i x j = k

j x k = i

k x i = j

For any two vectors a and b, we also have anticommutativity:

a x b = -(b x a)

(a) A = 2.0 i - 4.0 j + k, C = 3.0 i + 4.0 j + 10.0 k

A x C = 6.0 (i x i) - 12.0 (j x i) + 3.0 (k x i)

.......... + 8.0 (i x j) - 16.0 (j x j) - 4.0 (k x j)

.......... + 3.0 (k x i) + 4.0 (k x j) + 10.0 (k x k)

A x C = (4.0 + 4.0) i + (3.0 - 3.0) j + (12.0 + 8.0) k

A x C = 8.0 i + 20.0 k

With the same steps as in (a), we get

(b) A x C = 44.0 i + 17.0 j - 20.0 k

(c) A x C = -24.0 k

(d) A x C = -(C x A) = -18.0 i - 18.0 k