Answer to Question #118541 in Analytic Geometry for Joshua

Question

If α=3i−j+2k, , β=2i+j−k and γÌ…=i−2j+2k, find α×β×γ.
a.24i+7j-5k
b.-24i+7j-5k
c.24i+7j+5k
d.24i-7j-5k

Answer 1

$\alpha X \beta =\\\begin{vmatrix} i & j & k \\ 3 & -1 & 2 \\ 2 & 1 & -1 \end{vmatrix}$

= i(1-2)-j(-3-4)+k(3+2)

= -i +7j +5k

$\alpha X \beta X \gamma =\\\begin{vmatrix} i & j & k \\ -1 & 7 & 5 \\ 1 & -2 & 2 \end{vmatrix}$

= i(14+10) -j(-2-5) +k (2-7)

= 24i + 7j -5k

Option A is correct