Q. The equation of the line passing through the points $a_{1}\widehat{\mathbf{i}} + a_{2}\widehat{\mathbf{j}} + a_{3}\widehat{\mathbf{k}}\ and\ b_{1}\widehat{\mathbf{i}} + b_{2}\widehat{\mathbf{j}} + b_{3}\widehat{\mathbf{k}}$ is
A) $\left( a_{1}\widehat{\mathbf{i}} + a_{2}\widehat{\mathbf{j}} + a_{3}\widehat{\mathbf{k}} \right) + t(\ b_{1}\widehat{\mathbf{i}} + b_{2}\widehat{\mathbf{j}} + b_{3}\widehat{\mathbf{k}}\mathbf{)}$
B) $\left( \ a_{1}\widehat{\mathbf{i}} + a_{2}\widehat{\mathbf{j}} + a_{3}\widehat{\mathbf{k}}\ \right) - t(b_{1}\widehat{\mathbf{i}} + b_{2}\widehat{\mathbf{j}} + b_{3}\widehat{\mathbf{k}})$
C) $a_{1}(1 - t)\widehat{\mathbf{i}} + a_{2}(1 - t)\widehat{\mathbf{j}} + a_{3}(1 - t)\widehat{\mathbf{k}} + (\ b_{1}\widehat{\mathbf{i}} + b_{2}\widehat{\mathbf{j}} + b_{3}\widehat{\mathbf{k}})t$
D) None of the above
Explanation
(c)
Equation of straight line passing through the points
$a_{1}\widehat{\mathbf{i}} + a_{2}\widehat{\mathbf{j}} + a_{3}\widehat{\mathbf{k}}\mathbf{\ }and\ b_{1}\widehat{\mathbf{i}} + b_{2}\widehat{\mathbf{j}}\mathbf{+}b_{3}\widehat{\mathbf{k}}$ is
$a_{1}(1 - t)\widehat{\mathbf{i}} + a_{2}(1 - t)\widehat{\mathbf{j}} + a_{3}(1 - t)\widehat{\mathbf{k}} + \left( b_{1}\widehat{\mathbf{i}} + b_{2}\widehat{\mathbf{j}} + b_{3}\widehat{\mathbf{k}} \right)t$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.