Question

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

Answer 1

Answer:

$(\vec a \times\vec b)\times \vec c=5\hat i +15 \hat j-10\hat k$

| a×(b×c)|=$5\sqrt{14}$

Step-by-step explanation:

As $\vec a=\hat i-2\hat j+3\hat k\\\\\vec b=2\hat i+\hat j+\hat k\\\\\\\vec a \times \vec b=\left|\begin{array}{ccc}\hat i&\hat j&\hat k\\1&-2&3\\2&1&1\end{array}\right| \\\\=\hat i(-2-3)-\hat j(1-6)+\hat k(1+4)\\\\=-5\hat i+5\hat j+5\hat k$

Now for

$(\vec a \times\vec b)\times \vec c=(-5\hat i+5\hat j+5\hat k)\times(\hat i+\hat j+2\hat k)\\\\( \vec a\times\vec b)\times \vec c=\left|\begin{array}{ccc}\hat i&\hat j&\hat k\\-5&5&5\\1&1&2\end{array}\right|\\\\\\=\hat i(10-5)-\hat j(-10-5)+\hat k(-5-5)\\\\\\=5\hat i +15 \hat j-10\hat k$

For magnitude of

| a×(b×c)|=

$\sqrt{5^{2}+10^{2}+5^{2}   } \\\\=\sqrt{25+225+100} \\\\=\sqrt{350}\\\\=5\sqrt{14}$