88015 If \(\theta\) is the angle between the vectors \(\vec{a}=2 \hat{i}+2 \hat{j}-\hat{k}\) and \(\vec{b}=6 \hat{i}-3 \hat{j}+2 \hat{k}\) then

88016 If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three vectors, such that \(|\vec{a}+\vec{b}+\vec{c}|=0,|\vec{a}|=1,|\vec{b}|=2,|\vec{c}|=3\) then \(\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}}\) is equal to

88017 If the vectors \(a \hat{i}-2 \hat{j}+3 \hat{k}\) and \(3 \hat{i}+6 \hat{j}-5 \hat{k}\) are perpendicular to each other, then \(a\) is given by

88019 If the vectors \(\hat{i}-3 \hat{j}+2 \hat{k},-\hat{i}+2 \hat{j}\) represents the diagonals of a parallelogram, then its area will be

88015 If \(\theta\) is the angle between the vectors \(\vec{a}=2 \hat{i}+2 \hat{j}-\hat{k}\) and \(\vec{b}=6 \hat{i}-3 \hat{j}+2 \hat{k}\) then

88016 If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three vectors, such that \(|\vec{a}+\vec{b}+\vec{c}|=0,|\vec{a}|=1,|\vec{b}|=2,|\vec{c}|=3\) then \(\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}}\) is equal to

88017 If the vectors \(a \hat{i}-2 \hat{j}+3 \hat{k}\) and \(3 \hat{i}+6 \hat{j}-5 \hat{k}\) are perpendicular to each other, then \(a\) is given by

88019 If the vectors \(\hat{i}-3 \hat{j}+2 \hat{k},-\hat{i}+2 \hat{j}\) represents the diagonals of a parallelogram, then its area will be

88015 If \(\theta\) is the angle between the vectors \(\vec{a}=2 \hat{i}+2 \hat{j}-\hat{k}\) and \(\vec{b}=6 \hat{i}-3 \hat{j}+2 \hat{k}\) then

88016 If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three vectors, such that \(|\vec{a}+\vec{b}+\vec{c}|=0,|\vec{a}|=1,|\vec{b}|=2,|\vec{c}|=3\) then \(\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}}\) is equal to

88017 If the vectors \(a \hat{i}-2 \hat{j}+3 \hat{k}\) and \(3 \hat{i}+6 \hat{j}-5 \hat{k}\) are perpendicular to each other, then \(a\) is given by

88019 If the vectors \(\hat{i}-3 \hat{j}+2 \hat{k},-\hat{i}+2 \hat{j}\) represents the diagonals of a parallelogram, then its area will be

88015 If \(\theta\) is the angle between the vectors \(\vec{a}=2 \hat{i}+2 \hat{j}-\hat{k}\) and \(\vec{b}=6 \hat{i}-3 \hat{j}+2 \hat{k}\) then

88016 If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three vectors, such that \(|\vec{a}+\vec{b}+\vec{c}|=0,|\vec{a}|=1,|\vec{b}|=2,|\vec{c}|=3\) then \(\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{b}} \times \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}} \times \overrightarrow{\mathbf{a}}\) is equal to

88017 If the vectors \(a \hat{i}-2 \hat{j}+3 \hat{k}\) and \(3 \hat{i}+6 \hat{j}-5 \hat{k}\) are perpendicular to each other, then \(a\) is given by

88019 If the vectors \(\hat{i}-3 \hat{j}+2 \hat{k},-\hat{i}+2 \hat{j}\) represents the diagonals of a parallelogram, then its area will be