87806 Let \(u\) be a vector coplanar with the vectors \(\mathbf{a}=\mathbf{2} \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{b}=\hat{\mathbf{j}}+\hat{\mathbf{k}}\). If \(\mathbf{u} \quad\) is perpendicular to \(a\) and \(u\). \(b=24\), then \(|u|^2\) is equal to

87807 Let \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\sqrt{2} \hat{\mathbf{k}}, \overrightarrow{\mathbf{b}}=\overrightarrow{\mathbf{b}}_1 \hat{\mathbf{i}}+\overrightarrow{\mathbf{b}}_2 \hat{\mathbf{j}}+\sqrt{2} \hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}=5 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\sqrt{2} \hat{\mathbf{k}}\) be three vectors such that the projection vector of \(b\) on \(a\) is \(a\). If \(a+b\) is perpendicular to \(c\), then \(|\mathbf{b}|\) is equal to

87808 In a triangle \(\mathrm{ABC}\), if \(|\mathrm{BC}|=8,|\mathrm{CA}|=7,|\mathrm{AB}|=\) 10 , then the projection of the vector \(A B\) on \(A C\) is equal to

87809 If \(a, b\) and \(c\) are three non-zero vectors such that no two of these are collinear. If the vector \(a+2 b\) is collinear with \(c\) and \(b+3 c\) is collinear with a ( \(\lambda\) being some non-zero scalar). then a + \(2 b+6 c\) equal to

87806 Let \(u\) be a vector coplanar with the vectors \(\mathbf{a}=\mathbf{2} \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{b}=\hat{\mathbf{j}}+\hat{\mathbf{k}}\). If \(\mathbf{u} \quad\) is perpendicular to \(a\) and \(u\). \(b=24\), then \(|u|^2\) is equal to

87807 Let \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\sqrt{2} \hat{\mathbf{k}}, \overrightarrow{\mathbf{b}}=\overrightarrow{\mathbf{b}}_1 \hat{\mathbf{i}}+\overrightarrow{\mathbf{b}}_2 \hat{\mathbf{j}}+\sqrt{2} \hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}=5 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\sqrt{2} \hat{\mathbf{k}}\) be three vectors such that the projection vector of \(b\) on \(a\) is \(a\). If \(a+b\) is perpendicular to \(c\), then \(|\mathbf{b}|\) is equal to

87808 In a triangle \(\mathrm{ABC}\), if \(|\mathrm{BC}|=8,|\mathrm{CA}|=7,|\mathrm{AB}|=\) 10 , then the projection of the vector \(A B\) on \(A C\) is equal to

87809 If \(a, b\) and \(c\) are three non-zero vectors such that no two of these are collinear. If the vector \(a+2 b\) is collinear with \(c\) and \(b+3 c\) is collinear with a ( \(\lambda\) being some non-zero scalar). then a + \(2 b+6 c\) equal to

87806 Let \(u\) be a vector coplanar with the vectors \(\mathbf{a}=\mathbf{2} \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{b}=\hat{\mathbf{j}}+\hat{\mathbf{k}}\). If \(\mathbf{u} \quad\) is perpendicular to \(a\) and \(u\). \(b=24\), then \(|u|^2\) is equal to

87807 Let \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\sqrt{2} \hat{\mathbf{k}}, \overrightarrow{\mathbf{b}}=\overrightarrow{\mathbf{b}}_1 \hat{\mathbf{i}}+\overrightarrow{\mathbf{b}}_2 \hat{\mathbf{j}}+\sqrt{2} \hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}=5 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\sqrt{2} \hat{\mathbf{k}}\) be three vectors such that the projection vector of \(b\) on \(a\) is \(a\). If \(a+b\) is perpendicular to \(c\), then \(|\mathbf{b}|\) is equal to

87808 In a triangle \(\mathrm{ABC}\), if \(|\mathrm{BC}|=8,|\mathrm{CA}|=7,|\mathrm{AB}|=\) 10 , then the projection of the vector \(A B\) on \(A C\) is equal to

87809 If \(a, b\) and \(c\) are three non-zero vectors such that no two of these are collinear. If the vector \(a+2 b\) is collinear with \(c\) and \(b+3 c\) is collinear with a ( \(\lambda\) being some non-zero scalar). then a + \(2 b+6 c\) equal to

87806 Let \(u\) be a vector coplanar with the vectors \(\mathbf{a}=\mathbf{2} \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{b}=\hat{\mathbf{j}}+\hat{\mathbf{k}}\). If \(\mathbf{u} \quad\) is perpendicular to \(a\) and \(u\). \(b=24\), then \(|u|^2\) is equal to

87807 Let \(\overrightarrow{\mathbf{a}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\sqrt{2} \hat{\mathbf{k}}, \overrightarrow{\mathbf{b}}=\overrightarrow{\mathbf{b}}_1 \hat{\mathbf{i}}+\overrightarrow{\mathbf{b}}_2 \hat{\mathbf{j}}+\sqrt{2} \hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}=5 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\sqrt{2} \hat{\mathbf{k}}\) be three vectors such that the projection vector of \(b\) on \(a\) is \(a\). If \(a+b\) is perpendicular to \(c\), then \(|\mathbf{b}|\) is equal to

87808 In a triangle \(\mathrm{ABC}\), if \(|\mathrm{BC}|=8,|\mathrm{CA}|=7,|\mathrm{AB}|=\) 10 , then the projection of the vector \(A B\) on \(A C\) is equal to

87809 If \(a, b\) and \(c\) are three non-zero vectors such that no two of these are collinear. If the vector \(a+2 b\) is collinear with \(c\) and \(b+3 c\) is collinear with a ( \(\lambda\) being some non-zero scalar). then a + \(2 b+6 c\) equal to