The angle between two vectors given by $6\hat i + 6\hat j – 3\hat k$ and $7\hat i + 4\hat j + 4\hat k$ is

What will be the projection of vector $A=\hat{i}+\hat{j}+\hat{k}$ on vector $\vec{B}=\hat{i}+\hat{j}$.

$\overrightarrow A $ and $\overrightarrow B $ are two vectors given by $\overrightarrow A  = 2\widehat i + 3\widehat j$ and $\overrightarrow B  = \widehat i + \widehat j$. The magnitude of  the component (projection) of $\overrightarrow A$ on $\overrightarrow  B$ is

If $\overrightarrow{ P }=3 \hat{ i }+\sqrt{3} \hat{ j }+2 \hat{ k }$ and $\overrightarrow{ Q }=4 \hat{ i }+\sqrt{3} \hat{ j }+2.5 \hat{ k }$ then, The unit vector in the direction of $\overrightarrow{ P } \times \overrightarrow{ Q }$ is $\frac{1}{x}(\sqrt{3} \hat{i}+\hat{j}-2 \sqrt{3} \hat{k})$. The value of $x$ is

Two adjacent sides of a parallelogram are represented by the two vectors $\hat i + 2\hat j + 3\hat k$ and $3\hat i – 2\hat j + \hat k$. What is the area of parallelogram