If $a = i - 2j$ and $b = 2i + \lambda j$ are parallel,then $\lambda$ is

If $\overline{r} = -4 \hat{i} - 6 \hat{j} - 2 \hat{k}$ is a linear combination of the vectors $\overline{a} = -\hat{i} - 4 \hat{j} + 3 \hat{k}$ and $\overline{b} = -8 \hat{i} - \hat{j} + 3 \hat{k}$,then which of the following is true?

If $a = i + 2j + 2k$ and $b = 3i + 6j + 2k,$ then a vector in the direction of $a$ and having magnitude as $|b|$ is

If $\vec{a}=4 \hat{i}+13 \hat{j}-18 \hat{k}$,$\vec{b}=\hat{i}-2 \hat{j}+3 \hat{k}$,and $\vec{c}=2 \hat{i}+3 \hat{j}-4 \hat{k}$ are three vectors such that $\vec{a}=x \vec{b}+y \vec{c}$,then $x+y=$

If $a$ and $b$ are two non-zero and non-collinear vectors,then $a + b$ and $a - b$ are:

The value of $\hat{k} \cdot (\hat{i} \times \hat{j}) + \hat{i} \cdot (\hat{j} \times \hat{k})$ is . . . . . . .