Question

If a= 3i-j+2k ,b= 2i+j-k and c= i-2j+2k then, find the value of a.(b×c).

Answer 1

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Answer 2

a= 3i-j+2k ,b= 2i+j-k and c= i-2j+2k

To find:

a.(b×c)

Let us first consider,

(b × c) = (2i+j-k) × (i-2j+2k)

$\begin{pmatrix}2&1&-1\end{pmatrix}\times \begin{pmatrix}1&-2&2\end{pmatrix}\\\\=\begin{pmatrix}1\cdot \:2-\left(-1\cdot \left(-2\right)\right)&-1\cdot \:1-2\cdot \:2&2\left(-2\right)-1\cdot \:1\end{pmatrix}\\\\=\begin{pmatrix}0&-5&-5\end{pmatrix}$

a. (b×c) = (3i-j+2k) . (-5j-5k)

= 0 + 5 - 10

= - 5

∴ a.(b×c) = -5