Question

If vector a = 2i + 5j - 7j, b = -3i + 4j + k and c = i - 2j - 3k, compute (a x b) x c and a x (b x c) and verify that these are not equal.

Answer 1

Given  \(\vec a=2\hat i +5\hat j-7\hat k,\)  \(\vec b=-3\hat i+4\hat j+\hat k\)  and  \(\vec a=\hat i-2\hat j-3\hat k\)

We need to find  \((\vec a\times\vec b)\times\vec c.\)

First, we will find  \(\vec a\times\vec b\).

Recall the cross product of two vectors

Here, we have (a₁, a₂, a₃) = (2, 5, –7) and (b₁, b₂, b₃) = (–3, 4, 1)

Now, we will find \((\vec a\times\vec b)\times\vec c.\)

Using the formula for cross product as above, we have

Now, we need to find  \(\vec a\times(\vec b\times\vec c).\)

First, we will find \(\vec b\times\vec c.\)

Using the formula for cross product, we have

Now, we will find  \(\vec a\times(\vec b\times\vec c).\)

Using the formula for the cross product as above, we have

Therefore, we have

\((\vec a\times\vec b)\times\vec c\neq\) \(\vec a\times(\vec b\times\vec c)\).