87899 If \(\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}, \vec{b}=3 \hat{i}-\hat{j}+2 \hat{k}, \vec{c}=\hat{i}+3 \hat{j}+\hat{k}\) and \(\overrightarrow{\mathbf{a}}+\lambda \overrightarrow{\mathbf{b}}\) is perpendicular to \(\overrightarrow{\mathbf{c}}\), then \(\lambda=\)

87900 If vectors \(\overrightarrow{\mathbf{a}}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}+3 \hat{k}, \vec{b}=-\hat{i}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are such that, \(\overrightarrow{\mathbf{a}}+\lambda \overrightarrow{\mathbf{b}} \quad\) is perpendicular to \(\overrightarrow{\mathbf{c}}\), then \(\boldsymbol{\lambda}=\)

87875 If the position vectors of the vertices \(A, B\) and \(C\) of \(\triangle A B C\) are \(\hat{i}+2 \hat{j}-5 \hat{k},-2 \hat{i}+2 \hat{j}+\hat{k}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\) respectively, then \(\angle \mathrm{B}=\)

87883 The unit vector in the direction of the vector \(\overrightarrow{\mathbf{a}}+\mathbf{2} \overrightarrow{\mathbf{b}}-\overrightarrow{\mathbf{c}}\) is equal to

87899 If \(\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}, \vec{b}=3 \hat{i}-\hat{j}+2 \hat{k}, \vec{c}=\hat{i}+3 \hat{j}+\hat{k}\) and \(\overrightarrow{\mathbf{a}}+\lambda \overrightarrow{\mathbf{b}}\) is perpendicular to \(\overrightarrow{\mathbf{c}}\), then \(\lambda=\)

87900 If vectors \(\overrightarrow{\mathbf{a}}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}+3 \hat{k}, \vec{b}=-\hat{i}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are such that, \(\overrightarrow{\mathbf{a}}+\lambda \overrightarrow{\mathbf{b}} \quad\) is perpendicular to \(\overrightarrow{\mathbf{c}}\), then \(\boldsymbol{\lambda}=\)

87875 If the position vectors of the vertices \(A, B\) and \(C\) of \(\triangle A B C\) are \(\hat{i}+2 \hat{j}-5 \hat{k},-2 \hat{i}+2 \hat{j}+\hat{k}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\) respectively, then \(\angle \mathrm{B}=\)

87883 The unit vector in the direction of the vector \(\overrightarrow{\mathbf{a}}+\mathbf{2} \overrightarrow{\mathbf{b}}-\overrightarrow{\mathbf{c}}\) is equal to

87899 If \(\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}, \vec{b}=3 \hat{i}-\hat{j}+2 \hat{k}, \vec{c}=\hat{i}+3 \hat{j}+\hat{k}\) and \(\overrightarrow{\mathbf{a}}+\lambda \overrightarrow{\mathbf{b}}\) is perpendicular to \(\overrightarrow{\mathbf{c}}\), then \(\lambda=\)

87900 If vectors \(\overrightarrow{\mathbf{a}}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}+3 \hat{k}, \vec{b}=-\hat{i}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are such that, \(\overrightarrow{\mathbf{a}}+\lambda \overrightarrow{\mathbf{b}} \quad\) is perpendicular to \(\overrightarrow{\mathbf{c}}\), then \(\boldsymbol{\lambda}=\)

87875 If the position vectors of the vertices \(A, B\) and \(C\) of \(\triangle A B C\) are \(\hat{i}+2 \hat{j}-5 \hat{k},-2 \hat{i}+2 \hat{j}+\hat{k}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\) respectively, then \(\angle \mathrm{B}=\)

87883 The unit vector in the direction of the vector \(\overrightarrow{\mathbf{a}}+\mathbf{2} \overrightarrow{\mathbf{b}}-\overrightarrow{\mathbf{c}}\) is equal to

87899 If \(\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}, \vec{b}=3 \hat{i}-\hat{j}+2 \hat{k}, \vec{c}=\hat{i}+3 \hat{j}+\hat{k}\) and \(\overrightarrow{\mathbf{a}}+\lambda \overrightarrow{\mathbf{b}}\) is perpendicular to \(\overrightarrow{\mathbf{c}}\), then \(\lambda=\)

87900 If vectors \(\overrightarrow{\mathbf{a}}=\mathbf{2} \hat{\mathbf{i}}+\mathbf{2} \hat{\mathbf{j}}+3 \hat{k}, \vec{b}=-\hat{i}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\overrightarrow{\mathbf{c}}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are such that, \(\overrightarrow{\mathbf{a}}+\lambda \overrightarrow{\mathbf{b}} \quad\) is perpendicular to \(\overrightarrow{\mathbf{c}}\), then \(\boldsymbol{\lambda}=\)

87875 If the position vectors of the vertices \(A, B\) and \(C\) of \(\triangle A B C\) are \(\hat{i}+2 \hat{j}-5 \hat{k},-2 \hat{i}+2 \hat{j}+\hat{k}\) and \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\) respectively, then \(\angle \mathrm{B}=\)

87883 The unit vector in the direction of the vector \(\overrightarrow{\mathbf{a}}+\mathbf{2} \overrightarrow{\mathbf{b}}-\overrightarrow{\mathbf{c}}\) is equal to