List of top Mathematics Questions on Three Dimensional Geometry asked in GUJCET

Direction ratios of x-axis are:
The vector equation of the line passing through the point \( (1,2,-4) \) and perpendicular to the two lines \[ \frac{x-8}{3} = \frac{y+19}{-16} = \frac{z-10}{7} \] and \[ \frac{x-15}{3} = \frac{y-29}{8} = \frac{z-5}{-5} \] is _____
If the lines \[ \frac{1-x}{3} = \frac{7y-14}{2p} = \frac{3-z}{-2} \] and \[ \frac{7-7x}{3p} = \frac{y-5}{1} = \frac{6-z}{5} \] are perpendicular, then the value of \( p \) is _____
The angle between the pair of lines given by \[ \vec{r} = 3\hat{i} + 2\hat{j} - 4\hat{k} + \lambda(\hat{i} + 2\hat{j} + 2\hat{k}) \] and \[ \vec{r} = 5\hat{i} - 2\hat{j} + \mu(3\hat{i} + 2\hat{j} + 6\hat{k}) \] is _____
The area of the triangle with vertices \( A(1,1,2), B(2,3,5) \) and \( C(1,5,5) \) is _____