List of top Mathematics Questions on Vector Algebra asked in AP EAMCET

The point of intersection of the lines
\[ \vec r=2\vec b+t(6\vec c-\vec a) \] and
\[ \vec r=\vec a+s(\vec b-3\vec c) \] is

In quadrilateral \(ABCD\),
\[ \overrightarrow{AB}=\vec a, \qquad \overrightarrow{BC}=\vec b, \qquad \overrightarrow{DA}=\vec a-\vec b \] \(M\) is the midpoint of \(BC\) and \(X\) is a point on \(DM\) such that
\[ \overrightarrow{DX}=\frac45\overrightarrow{DM}. \] Then the points \(A,X,C\)

Let \(\vec a=x\hat i+y\hat j+z\hat k\) and \(x=2y\). If \(|\vec a|=5\sqrt2\) and \(\vec a\) makes an angle of \(135^\circ\) with the \(z\)-axis, then \(\vec a=\)

Let \(\vec a,\vec b,\vec c\) be the position vectors of the vertices of a triangle \(ABC\). Through the vertices, lines are drawn parallel to the sides to form the triangle \(A'B'C'\). Then the centroid of \(\triangle A'B'C'\) is