(a \times \lbrack a \times (a \times \mathbf{b})\rbrack) is... | MATH - VECTOR TRIPLE PRODUCT | SolveeIt

Question

$a \times \lbrack a \times (a \times \mathbf{b})\rbrack$ is equal to

$(a \times a).(b \times a)$

$a.(b \times a) - b.(a \times b)$

$\lbrack a.(a \times b)\rbrack a$

$(a.a)(b \times a)$

Answer

$(a.a)(b \times a)$

Explanation

Solution

$\mathbf{a} \times \lbrack\mathbf{a} \times (\mathbf{a} \times \mathbf{b})\rbrack = \mathbf{a} \times \{(\mathbf{a}.\mathbf{b})\mathbf{a} - (\mathbf{a}.\mathbf{a})\mathbf{b}\} = (\mathbf{a}.\mathbf{b})(\mathbf{a} \times \mathbf{a}) - (\mathbf{a}.\mathbf{a})(\mathbf{a} \times \mathbf{b}) = (\mathbf{a}.\mathbf{b})0 + (\mathbf{a}.\mathbf{a})(\mathbf{b} \times \mathbf{a})$

$= (\mathbf{a}.\mathbf{a})(\mathbf{b} \times \mathbf{a})$ .

Question: \(a \times \lbrack a \times (a \times \mathbf{b})\rbrack\) is equal to...

Solution