Question

If a = i - 2j - 3k, b = 2i + j - k and c = i + 3 j - 2k, verify that a × (b × c) ≠ (a × b) × c.

Answer 1

Answer:

It is verified that a × (b × c) ≠ (a × b) × c.

Step-by-step explanation:

If $\vec a = \hat i - 2\hat j - 3\hat k$

$\vec b = 2\hat i + \hat j - \hat k$ and

$\vec c =\hat i + 3\hat j - 2\hat k$

To verify that a × (b × c) ≠ (a × b) × c,we first calculate  a × (b × c)

(b × c)=

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

Now for a × (b × c)=

$\left|\begin{array}{ccc}\hat i&\hat j&\hat k\\1&-2&-3\\1&3&5\end{array}\right| \\\\=(-10+9)\hat i-(5+3)\hat j+(3+2)\hat k\\\\=-\hat i-7\hat j+5\hat k$.....eq1

(a × b)=

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

for (a × b) × c=

$\left|\begin{array}{ccc}\hat i&\hat j&\hat k\\5&-5&5\\1&3&-2\end{array}\right| \\\\=(10-15)\hat i-(-10-5)\hat j+(15+5)\hat k\\\\=-5\hat i+15\hat j+20\hat k$....eq2

It is clear from eq1 and eq2 that a × (b × c) ≠ (a × b) × c

Answer 2

Answer:

They are not equal.

Step-by-step explanation:

they are not equal