87966 If \(\vec{a}, \vec{b}, \vec{c}\) are unit vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\), then \(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}} \cdot \overrightarrow{\mathrm{a}}=\)

87967 If \((\vec{a} \times \vec{b})^2+(a . \vec{b})^2=144\) and \(|\vec{a}|=4\), then \(|\vec{b}|=\)

87969 The projection of \(\vec{a}=3 \hat{i}-\hat{j}+5 \hat{k}\) on \(\overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+3 \hat{\mathbf{j}}+\hat{\mathrm{k}}\) is

87970 If \(\vec{a}\) is vector perpendicular to both \(\vec{b}\) and \(\overrightarrow{\mathbf{c}}\), then

87966 If \(\vec{a}, \vec{b}, \vec{c}\) are unit vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\), then \(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}} \cdot \overrightarrow{\mathrm{a}}=\)

87967 If \((\vec{a} \times \vec{b})^2+(a . \vec{b})^2=144\) and \(|\vec{a}|=4\), then \(|\vec{b}|=\)

87969 The projection of \(\vec{a}=3 \hat{i}-\hat{j}+5 \hat{k}\) on \(\overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+3 \hat{\mathbf{j}}+\hat{\mathrm{k}}\) is

87970 If \(\vec{a}\) is vector perpendicular to both \(\vec{b}\) and \(\overrightarrow{\mathbf{c}}\), then

87966 If \(\vec{a}, \vec{b}, \vec{c}\) are unit vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\), then \(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}} \cdot \overrightarrow{\mathrm{a}}=\)

87967 If \((\vec{a} \times \vec{b})^2+(a . \vec{b})^2=144\) and \(|\vec{a}|=4\), then \(|\vec{b}|=\)

87969 The projection of \(\vec{a}=3 \hat{i}-\hat{j}+5 \hat{k}\) on \(\overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+3 \hat{\mathbf{j}}+\hat{\mathrm{k}}\) is

87970 If \(\vec{a}\) is vector perpendicular to both \(\vec{b}\) and \(\overrightarrow{\mathbf{c}}\), then

87966 If \(\vec{a}, \vec{b}, \vec{c}\) are unit vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\), then \(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathbf{c}}+\overrightarrow{\mathbf{c}} \cdot \overrightarrow{\mathrm{a}}=\)

87967 If \((\vec{a} \times \vec{b})^2+(a . \vec{b})^2=144\) and \(|\vec{a}|=4\), then \(|\vec{b}|=\)

87969 The projection of \(\vec{a}=3 \hat{i}-\hat{j}+5 \hat{k}\) on \(\overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+3 \hat{\mathbf{j}}+\hat{\mathrm{k}}\) is

87970 If \(\vec{a}\) is vector perpendicular to both \(\vec{b}\) and \(\overrightarrow{\mathbf{c}}\), then