CBSE Questions for Class 12 Commerce Maths Vector Algebra Quiz 14 - MCQExams.com

For any two vectors $$\vec{a} \space and \space \vec{b}, (\vec{a} \times \hat{i}) . (\vec{b} \times \hat{i}) + (\vec{a} \times \hat{j}) . (\vec{b} \times \vec{j}) + (\vec{a} \times \vec{k}) . (\vec{b} \times \vec{k})$$ is always equal to
  • $$\vec{a} . \vec{b}$$
  • $$2\vec{a} . \vec{b}$$
  • zero
  • none of these
The unit vector perpendicular to the vectors $$\hat i-\hat j$$ forming a right handed system is
  • $$\hat k$$
  • $$-\hat k$$
  • $$\dfrac {\hat i-\hat j}{\sqrt 2}$$
  • $$\dfrac {\hat i+\hat j}{\sqrt 2}$$
For any three vectors $$ \vec{a}, \vec{b} $$ and $$ \vec{c},(\vec{a}-\vec{b}) \cdot(\vec{b}-\vec{c}) \times(\vec{c}-\vec{a})=2 \vec{a} \cdot \vec{b} \times \vec{c} $$
  • True
  • False
0:0:1


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