List of top Mathematics Questions on Vectors asked in KEAM

If \( \vec{a} \) and \( \vec{b} \) are non-collinear unit vectors and \( |\vec{a} + \vec{b}|^2 = 3 \), then \( (3\vec{a} + 2\vec{b}) \cdot (3\vec{a} - \vec{b}) \) is equal to:
The equation of the plane through the point (1, 5, 3) and having a normal vector \(\hat n=2\hat i-2\hat j-\hat k\) is
If \(\bar{a}=2\hat{i}+3\hat{j}-4\hat{k}\) and \(\bar{b}=\hat{i}+3\hat{j}+2\hat{k}\), then a unit vector in the direction of \(\bar a +\bar b\) is
If \(\bar{a}\times\bar{b}=7\hat{i}+9\hat{j}+10\hat{k}\) and \(\bar{a}\cdot\bar{b}=-20\), then \(|\bar{a}|^{2}|\bar{b}|^{2}=\)
The vector equation of the line joining the points (2, 1, 3) and (-2, 4, 1) is
The angle between the lines \(\overrightarrow{r}=\hat{i}+4\hat{k}+\lambda(2\hat{i}+\hat{j}-\hat{k})\) and \(\overrightarrow{r}=2\hat{i}-\hat{j}+3\hat{k}+\mu(3\hat{i}+\hat{k})\) is
If the liner \(\overrightarrow{r}=2\hat{i}+\hat{j}+t(3\hat{i}+\hat{j}-2\hat{k})\) is parallel to the plane 2x+4y+az=8, then the value of a is equal to
If \(\overrightarrow{a}=\hat{i}+\lambda\hat{j}-2\hat{k}, \overrightarrow{b}=2\hat{i}-3\hat{j}+5\hat{k}\ and\ \overrightarrow{a}\cdot\overrightarrow{b}=-20\), then the value of \(\lambda\) is equal to
If \(|\overrightarrow{a}|=3,|\overrightarrow{b}|=4\) and \(|\overrightarrow{a}-\overrightarrow{b}|=\sqrt7\), then \(\overrightarrow{a}\cdot\overrightarrow{b}\) is equal to
The position of a particle is given by $ r =\hat{i}+2\hat{j}-\hat{k} $ and its linear momentum is given by $ p = 3\hat{i}+4\hat{j}-2\hat{k} $ . Then its angular momentum, about the origin is perpendicular to