Vector Algebra ...

Six vectors, a through f have the magnitudes and directions indicated in the figure. Which of the following statements is true?

If $$2\vec{a}+3\vec{b}-5\vec{c}=\vec{0}$$, then ratio in which $$\vec{c}$$ divides $$\vec{AB}$$ is

Let $$ABCD$$ be a parallelogram whose diagonals intersect at $$P$$ and $$O$$ be the origin, then $$\vec { OA } +\vec { OB } +\vec { OC } +\vec { OD } $$ equals

The projection of $$\displaystyle \overset { \rightarrow  }{ a } =2\overset { \wedge  }{ i } +3\overset { \wedge  }{ j } -2\overset { \wedge  }{ k } $$ on $$\displaystyle \overset { \rightarrow  }{ b } =\overset { \wedge  }{ i } +2\overset { \wedge  }{ j } +3\overset { \wedge  }{ k } $$ is:

If $$\vec {a}$$ is a nonzero vector of magnitude $$'a'$$ and $$\lambda$$ a nonzero scalar, then $$\lambda{\vec {a}}$$ is unit vector if

Find $$u+v$$, when $$u=(3,4,-2)$$ and $$v=(0,-4,0)$$.

Find the vector $$w$$ with the initial point $$(9,4)$$ and final point $$(12,6)$$.

Give the vector from $$(2,-7,0)$$ to $$(1,-3,-5)$$.

Find the vector which joins the point A$$(4,5,6)$$ to B$$(10,11,12)$$.

Give the vector from $$(1,-3,-5)$$ to $$(2,-7,0)$$.