Vector Algebra ...

If the vectors a, b and c form the sides be the sides AB, CA, and AB respectively of a triangle ABC, then

If $$\vec{a}, \vec{b}, \vec{c}$$ are three non coplanar vectors, then $$(\vec{a}+\vec{b}+\vec{c})[(\vec{a}+\vec{b}) \times (\vec{a}+\vec{c})] $$ is :

Two or more vectors having the same initial point are

Given the points $$A(-2,3,4),B(3,2,5),C(1,-1,2),\,\&\,D(3,2,-4)$$ The projection of the vector $$\displaystyle \underset{AB}{\rightarrow}$$ on the vector $$\displaystyle \underset{CD}{\rightarrow}$$ is

The sum of two forces is $$18$$ N and resultant whose direction is at right angles to the smaller force is $$12$$N. The magnitude of the two forces are

If O is origin and C is the mid point of $$A(2, -1)$$ and $$B(-4,3)$$. Then value of OC is

Given that u is a vector of length $$2$$, v is a vector of length $$3$$ and the angle between them when placed tail to tail is $$\displaystyle 45^{\circ} $$, which option is closest to the exact value of $$\vec u\cdot\vec v$$ ?

The figure formed by the four points i + j - k, 2i + 3j, 3i + 5j -2k and k - j is

ABCDEF is a regular hexagon . Let $$\displaystyle \vec { AB } =a$$ and $$\displaystyle \vec { BC } =b$$. Express the vectors $$\displaystyle \vec { AC } $$ in terms if a and b.

The system of vectors $$i, j, k$$ is