Consider two vectors ${\overrightarrow F _1} = 2\hat i + 5\hat k$ and ${\overrightarrow F _2} = 3\hat j + 4\hat k.$ The magnitude of the scalar product of these vectors is

The vectors from origin to the points $A$ and $B$ are $\overrightarrow A = 3\hat i - 6\hat j + 2\hat k$ and $\overrightarrow B = 2\hat i + \hat j - 2\hat k$ respectively. The area of the triangle $OAB$ be

Explain the kinds of multiplication operations for vectors.

The components of $\vec a = 2\hat i + 3\hat j$ along the direction of vector $\left( {\hat i + \hat j} \right)$ is

Two vector $A$ and $B$ have equal magnitudes. Then the vector $\mathop A\limits^ \to + \mathop B\limits^ \to $ is perpendicular to

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