Question

Simplify the following:i. (i - 2j + 3k) × (2i + j - k) . (j + k)ii. (2i - 3j + k) . (i - j + 2k) × (2i + j + k)

Answer 1

These are the questions of SCALAR TRIPLE PRODUCT

i. (i - 2j + 3k) × (2i + j - k) . (j + k)

Solution:

$=\left[\begin{array}{ccc}1&-2&3\\2&1&-1\\0&1&1\end{array}\right] \\=1(1+1)-(-2)(2-0)+3(2-0)\\=2+4+6\\=12$

ii. (2i - 3j + k) . (i - j + 2k) × (2i + j + k)

Solution:

$\left[\begin{array}{ccc}2&-3&1\\1&1&-2\\2&1&1\end{array}\right] \\\\=2(-1-2)-(-3)(1-4)+1(1-2)\\=2(-3)+3(-3)+1(-1)\\=-6-9-1\\=-16$