1.

If the equations of two lines L1 and L2 are \(\vec{r}=\vec{a_1}+λ\vec{b_1}\) and \(\vec{r}=\vec{a_2}+μ\vec{b_2}\), then which of the following is the correct formula for the angle between the two lines?(a) cos⁡θ=\(\left |\frac{\vec{a_1}.\vec{a_2}}{|\vec{b_1}||\vec{a_2}|}\right |\)(b) cos⁡θ=\(\left |\frac{\vec{a_1}.\vec{a_2}}{|\vec{a_1}||\vec{a_2}|}\right |\)(c) cos⁡θ=\(\left |\frac{\vec{b_1}.\vec{b_2}}{|\vec{b_1}||\vec{b_2}|}\right |\)(d) cos⁡θ=\(\left |\frac{\vec{a_1}.\vec{b_2}}{|\vec{a_1}||\vec{b_2}|}\right |\)I got this question at a job interview.Query is from Three Dimensional Geometry topic in section Three Dimensional Geometry of Mathematics – Class 12

Answer»

The correct option is (c) cos⁡θ=\(\left |\frac{\VEC{b_1}.\vec{b_2}}{|\vec{b_1}||\vec{b_2}|}\right |\)

The best explanation: Given that the EQUATIONS of the LINES are

\(\vec{r}=\vec{a_1}+λ\vec{b_1} \,and \,\vec{r}=\vec{a_2}+μ\vec{b_2}\)

∴ the ANGLE between the TWO lines is given by

cos⁡θ=\(\left |\frac{\vec{b_1}.\vec{b_2}}{|\vec{b_1}||\vec{b_2}|}\right |\).


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