Line Perpendicular to Two Lines (Jee Mains)

3D Line Equations and Skew

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Line Perpendicular to Two Lines

If the equation of the line passing through the point $\left( {0, - \frac{1}{2},0} \right)$ and perpendicular to the lines $\vec r = \lambda \left( {\hat i + a\hat j + b\hat k} \right)$ and $\vec r = \left( {\hat i - \hat j - 6\hat k} \right) + \mu \left( { - b\hat i + a\hat j + 5\hat k} \right)$ is $\frac{{x - 1}}{{ - 2}} = \frac{{y + 4}}{d} = \frac{{z - c}}{{ - 4}}$ , then a + b+ c+ d is equal to :

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