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

Let $a = i + 2j + k$,$b = i - j + k$,$c = i + j - k$. $A$ vector in the plane of $a$ and $b$ has projection $\frac{1}{\sqrt{3}}$ on $c$. Then,one such vector is

If the angle between the vectors $\vec{a} = 2\lambda^2 \hat{i} + 4\lambda \hat{j} + \hat{k}$ and $\vec{b} = 7\hat{i} - 2\hat{j} + \lambda \hat{k}$ is obtuse,then the values of $\lambda$ lie in:

If $a, b, c$ are three vectors such that $a \perp (b + c)$, $b \perp (c + a)$ and $c \perp (a + b)$, and $|a| = 1, |b| = 2, |c| = 3$, then $|a + b + c|$ is equal to:

The scalars $l$ and $m$ such that $la + mb = c,$ where $a, b$ and $c$ are given vectors,are equal to

If $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$, $|\vec{a}|=3$, $|\vec{b}|=5$, and $|\vec{c}|=7$, then the angle between $\vec{a}$ and $\vec{b}$ is