Vector Algebra ...

If $$\vec a$$ is a non-zero vector of modulus $$a$$ and $$m$$ is a non-zero scalar, then $$m \vec a$$ is a unit vector if

If vector $$\vec{a} = 2\hat i - 3\hat j + 6\hat k$$ and vector $$\vec{b} = - 2\hat i + 2\hat j - \hat k$$, then ratio of Projection of $$\vec a$$  on vector  $$\vec b$$ to Projection of  $$\vec b$$  on $$\vec a$$ is equal to

The projection of the line segment joining the points A(-1, 0, 3) and B(2, 5, 1) on the line whose direction ratios are proportional to 6, 2, 3, is

Let $$\vec {p}$$ is the position vector of the orthocentre & $$\vec {g}$$ is the position vector of the centroid of the triangle $$ABC$$ where circumcentre is the origin. If $$\vec {p}= K\vec{g},$$ then $$K=$$

If $$\vec{a}, \vec{b}  $$ and $$ \vec {c} $$ are three non- coplanar vectors, then the length of projection of vector $$\vec{a} $$ in the plane of the vectors $$\vec{b}$$ and $$\vec{c}$$ may be given by

Five coplanar forces (each of magnitude $$20N$$) are acting on a body. The angle between two neighboring forces have  the same value. The resultant of these forces is necessarily equal to

If the scalar projection of the vector $$x\hat i - \hat j + \hat k$$ on the vector $$2 \hat i - \hat j + 5\hat k$$ is $$ \dfrac{1}{\sqrt{30}}$$, then value of $$x$$ is equal to

A man starts from $$O$$ moves $$500m$$ turns by $$60 ^\circ$$ and moves $$500m$$ again turns by $$60 ^\circ$$ and moves $$500m$$ and so on. Find the displacement after $$(i)$$ 5th turn , $$(ii)$$ 3rd turn.

The projection of the vector $$\hat i - 2\hat j + \hat k$$ on the vector $$4\hat i - 4\hat j + 7\hat k$$ is

If the vector product of a constant vector $$\displaystyle \vec{OA}$$ with a variable vector $$\displaystyle \vec{OB}$$ in a fixed plane $$OAB$$ be a constant vector, then locus of $$B$$ is :