Consider the following for the next two (02) items that follow :

Consider two lines whose direction ratios are (2, -1, 2) and (k, 3, 5). They are inclined at an angle $\frac{\pi}{4}$

What are the direction ratios of a line which is perpendicular to both the lines ?

Consider the following for the next two (02) items that follow :

Let $\vec{a}=3 \hat{i}+3 \hat{j}+3 \hat{k} $ and $ \vec{c}=\hat{j}-\hat{k} \text {. Let } \vec{b}$ be such that $\vec{a} \cdot \vec{b}=27 $ and $ \vec{a} \times \vec{b}=\overrightarrow{9 c}$

What is $\vec{b}$ equal to ?

Consider the following for the next two (02) items that follow :

Let $\vec{a}=3 \hat{i}+3 \hat{j}+3 \hat{k} $ and $ \vec{c}=\hat{j}-\hat{k} \text {. Let } \vec{b}$ be such that $\vec{a} \cdot \vec{b}=27 $ and $ \vec{a} \times \vec{b}=\overrightarrow{9 c}$

What is the angle between $(\vec{a}+\vec{b})$ and $\vec{c}$ ?

Consider the following for the item that follow :

Let a vector $\vec{a}=4 \hat{i}-8 \hat{j}+\hat{k}$ make angles α, β, γ with the positive directions of x, y, z axes respectively. 

What is cosα equal to ?