Mathematics Vectors & 3D Geometry questions from JEE Main 2016.
In a triangle $ABC$, right angle at vertex $A$, if the position vectors of $A,B$ and $C$ are respectively $3\hat{i}+ \hat{j}- \hat{k}, -\hat{i}+3\hat{j}+p\hat{k}$ and $5\hat{i}+q\hat{j}-4\hat{k}$ , then the point $(p,q)$ lies on a line:
$ABC$ is a triangle in a plane with vertices $A(2, 3, 5), B(-1, 3, 2)$ and $C(\lambda , 5, \mu )$ . If the median through $A$ is equally inclined to the coordinate axes, then the value of $({\lambda }^{3}+{\mu }^{3}+5)$ is
Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three unit vectors such that $\vec{a} \times (\vec{b} \times \vec{c})=\frac{\sqrt{3}}{2}(\vec{b} + \vec{c}).$ If $\vec{b}$ is not parallel to $\vec{c}$ , then the angle between $\vec{a}$ and $\vec{b}$ is