Vector Algebra ...

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

Let P, Q, R and S be the points on the plane with position vectors (-2i - j), 4i, (3i + 3j) and (-3i + 2j) respectively. The quadilateral PQRS must be a

In triangle $$ABC$$, which of the following is not true?

$$\vec{a}\, \neq\, \bar{0},\,\vec{b}\,\neq\,\bar{0},\,\vec{c}\,\neq\,0,\,\vec{a}\,\times\,\vec{b}\,=\,\vec{0},\, \bar{b}\,\times\,\vec{c}\,=\,0\,\Rightarrow\,\vec{a}\,\times\,\vec{c}\,=$$

The position vectors of $$P$$ and $$Q$$ are respectively $$a$$ and $$b$$. If $$R$$ is a point on $$PQ$$, $$PQ$$ such that $$PR=5PQ$$, then the position vector of $$R$$ is

If $$|\vec {a}| = |\vec {b}| = 1$$ and $$|\vec {a} + \vec {b}| = \sqrt {3}$$, then the value of $$(3\vec {a} - 4\vec {b}) \cdot (2\vec {a} + 5\vec {b})$$ is

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

Let $$\overrightarrow {a} , \overrightarrow {b}$$ and $$\overrightarrow {c}$$ be vectors with magnitudes 3, 4 and 5 respectively and $$\overrightarrow{a} + \overrightarrow {b}+\overrightarrow {c}=\overrightarrow {0}$$, then the value of $$\overrightarrow{a}. \overrightarrow{b}+\overrightarrow{b}. \overrightarrow{c} + \overrightarrow{c}. \overrightarrow{a}$$ is

Find the correct vectorial relationship with the help of the figure above.

How much does a watch lose per day, if its hands coincide every $$64$$ minutes?