List of top Mathematics Questions on Product of Two Vectors asked in MET

If the vectors \( \vec{p} = (a+1)\hat{i} + a\hat{j} + a\hat{k},\ \vec{q} = a\hat{i} + (a+1)\hat{j} + a\hat{k} \) and \( \vec{r} = a\hat{i} + a\hat{j} + (a+1)\hat{k} \) are coplanar, then the value of \(a\) is _ _ _ _.

\([\vec{a} + \vec{b},\; \vec{b} + \vec{c},\; \vec{c} + \vec{a}]\) is equal to

The value of \(\{(\vec{a} \times \vec{b})^2 + (\vec{a}\cdot \vec{b})^2\\div a^2 b^2\) is}

\(\vec{a}=\frac{1}{7}(2\hat{i}+3\hat{j}+6\hat{k}),\; \vec{b}=\frac{1}{7}(3\hat{i}-\lambda \hat{j}+2\hat{k})\). If \(\vec{a}\perp \vec{b}\), find \(\lambda\)

The value of \(|\vec{a} \times \vec{b} + \vec{b} \times \vec{a}|\) is

The number of unit vectors perpendicular to \(\vec{a} = \hat{i}+\hat{j}\) and \(\vec{b} = \hat{j}+\hat{k}\) is:

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

Three concurrent edges of a parallelepiped are given by \[ \vec{a} = 2\hat{i} - 3\hat{j} + \hat{k},\quad \vec{b} = \hat{i} - \hat{j} + 2\hat{k},\quad \vec{c} = 2\hat{i} + \hat{j} - \hat{k}. \] The volume of the parallelepiped is:

The value of \( \vec{i} \cdot (\vec{j} \times \vec{k}) + \vec{j} \cdot (\vec{i} \times \vec{k}) + \vec{k} \cdot (\vec{i} \times \vec{j}) \) is:

If \( \vec{a} \) and \( \vec{b} \) are two unit vectors and \( \theta \) is the angle between them, then \( |\vec{a} + \vec{b}| \) is a unit vector if \( \theta \) is:

The value of \( \vec{a} \times (\vec{b} \times \vec{c}) \) is:

If \( |\vec{a}| = 3 \), \( |\vec{b}| = 4 \) and \( \vec{a} \cdot \vec{b} = 6 \), then the angle between \( \vec{a} \) and \( \vec{b} \) is:

The projection of vector \( \vec{a} = 2\vec{i} + 3\vec{j} + 2\vec{k} \) on vector \( \vec{b} = \vec{i} + 2\vec{j} + \vec{k} \) is:

The value of \( \vec{i} \cdot (\vec{j} \times \vec{k}) + \vec{j} \cdot (\vec{i} \times \vec{k}) + \vec{k} \cdot (\vec{i} \times \vec{j}) \) is:

The value of $[ \vec{i} + \vec{j}, \vec{j} + \vec{k}, \vec{k} + \vec{i} ]$ is:

The value of $[ \vec{i} + \vec{j}, \vec{j} + \vec{k}, \vec{k} + \vec{i} ]$ is: