The point of intersection of $r \times a = b \times a$ and $r \times b = a \times b$,where $a = i + j$ and $b = 2i - k$ is

If $\vec{a}$ and $\vec{b}$ are two unit vectors such that $\vec{a} + 2\vec{b}$ and $5\vec{a} - 4\vec{b}$ are perpendicular to each other,then the angle between $\vec{a}$ and $\vec{b}$ is ............. $^\circ$.

If the scalar projection of the vector $xi - j + k$ on the vector $2i - j + 5k$ is $\frac{1}{\sqrt{30}}$, then the value of $x$ is equal to

If $\bar{a}$ and $\bar{b}$ are unit vectors and $\theta$ is the angle between them,then $\tan(\theta/2) =$

If the line joining points $A$ and $B$ having position vectors $6 \vec{a}-4 \vec{b}+4 \vec{c}$ and $-4 \vec{c}$ respectively,and the line joining the points $C$ and $D$ having position vectors $-\vec{a}-2 \vec{b}-3 \vec{c}$ and $\vec{a}+2 \vec{b}-5 \vec{c}$ intersect,then their point of intersection is

If $|a| = 3$ and $|b| = 4$,for what value of $\lambda$ is the vector $(a + \lambda b)$ perpendicular to $(a - \lambda b)$?