List of top Mathematics Questions on Vectors asked in AP EAPCET

If the vector components of a vector \(\vec a\) along a vector \[ \vec b=4\hat i+5\hat j+3\hat k \] and perpendicular to \(\vec b\) are respectively \[ \frac{7}{25}(4\hat i+5\hat j+3\hat k) \] and \[ \frac{1}{25}(47\hat i-10\hat j-46\hat k), \] then \[ |\vec a|^2= \]

The vectors \[ \vec{a}=2\hat{i}+3\hat{j}+6\hat{k} \] and \(\vec{b}\) are collinear and \[ |\vec{b}|=21, \] then \(\vec{b}=\)

If \[ \vec{a}=(p,-2,5) \] and \[ \vec{b}=(1,q,-3) \] are collinear vectors then

Let \[ \vec{a}=2\hat{i}+3\hat{j}+\hat{k},\quad \vec{b}=4\hat{i}+\hat{j},\quad \vec{c}=\hat{i}-3\hat{j}-7\hat{k} \] If \[ \vec{r}=x\hat{i}+y\hat{j}+z\hat{k}, \] \[ \vec{r}\cdot\vec{a}=9,\quad \vec{r}\cdot\vec{b}=7,\quad \vec{r}\cdot\vec{c}=6, \] then \((x,y,z)=\)

If \(ABCD\) is a cyclic quadrilateral with \(R\) as the radius of the circumcircle and \[ (AB)^2+(CD)^2=4R^2, \] then

If \[ |\vec{a}|=13,\qquad |\vec{b}|=5 \] and \[ \vec{a}\cdot\vec{b}=60, \] then \[ |\vec{a}\times\vec{b}|= \]

If the position vectors of the points \(A,B,C,D\) are \[ 7\hat{i}-4\hat{j}+7\hat{k},\quad \hat{i}-6\hat{j}+10\hat{k},\quad -\hat{i}-3\hat{j}+4\hat{k},\quad 5\hat{i}-\hat{j}+5\hat{k} \] respectively, then \(ABCD\) is