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Question: If \(\mathbf{a}.\mathbf{i} = 4,\) then \((\mathbf{a} \times \mathbf{j}).(2\mathbf{j} - 3\mathbf{k}) ...

If a.i=4,\mathbf{a}.\mathbf{i} = 4, then (a×j).(2j−3k)=(\mathbf{a} \times \mathbf{j}).(2\mathbf{j} - 3\mathbf{k}) =

A

12

B

2

C

0

D

– 12

Answer

– 12

Explanation

Solution

(a×j).(2j−3k)=a.⥂{j×(2j−3k)}(\mathbf{a} \times \mathbf{j}).(2\mathbf{j} - 3\mathbf{k}) = \mathbf{a}. ⥂ \{\mathbf{j} \times (2\mathbf{j} - 3\mathbf{k})\}

=a.{−3(j×k)}=−3(a.i)=−12.= \mathbf{a}.\{ - 3(\mathbf{j} \times \mathbf{k})\} = - 3(\mathbf{a}.\mathbf{i}) = - 12.