87961 If \(|\vec{a}|=16,|\vec{b}|=4\), then \(\sqrt{|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2}=\)

87962 If \(\vec{a}=\hat{i}+\lambda \hat{j}+2 \hat{k} ; \vec{b}=\mu \hat{i}+\hat{j}-\hat{k}\) are orthogonal and \(|\overrightarrow{\mathbf{a}}|=|\overrightarrow{\mathbf{b}}|\), then \((\lambda, \mu)=\)

87963 If \(\vec{a}\) and \(\vec{b}\) are mutually perpendicular unit vectors, then \((3 \vec{a}+2 \vec{b}) \cdot(5 \vec{a}-6 \vec{b})=\)

87964 If \(\overrightarrow{\mathbf{a}}=2 \hat{\mathrm{i}}+\lambda \hat{\mathrm{j}}+\hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\) are orthogonal, then value of \(\lambda\) is

87965 Let \(\vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}\). If \(\vec{b}\) is a vector such that \(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathrm{b}}=|\overrightarrow{\mathrm{b}}|^2\) and \(|\overrightarrow{\mathbf{a}}-\overrightarrow{\mathrm{b}}|=\sqrt{7}\), then \(|\overrightarrow{\mathrm{b}}|=\)

87961 If \(|\vec{a}|=16,|\vec{b}|=4\), then \(\sqrt{|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2}=\)

87962 If \(\vec{a}=\hat{i}+\lambda \hat{j}+2 \hat{k} ; \vec{b}=\mu \hat{i}+\hat{j}-\hat{k}\) are orthogonal and \(|\overrightarrow{\mathbf{a}}|=|\overrightarrow{\mathbf{b}}|\), then \((\lambda, \mu)=\)

87963 If \(\vec{a}\) and \(\vec{b}\) are mutually perpendicular unit vectors, then \((3 \vec{a}+2 \vec{b}) \cdot(5 \vec{a}-6 \vec{b})=\)

87964 If \(\overrightarrow{\mathbf{a}}=2 \hat{\mathrm{i}}+\lambda \hat{\mathrm{j}}+\hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\) are orthogonal, then value of \(\lambda\) is

87965 Let \(\vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}\). If \(\vec{b}\) is a vector such that \(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathrm{b}}=|\overrightarrow{\mathrm{b}}|^2\) and \(|\overrightarrow{\mathbf{a}}-\overrightarrow{\mathrm{b}}|=\sqrt{7}\), then \(|\overrightarrow{\mathrm{b}}|=\)

87961 If \(|\vec{a}|=16,|\vec{b}|=4\), then \(\sqrt{|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2}=\)

87962 If \(\vec{a}=\hat{i}+\lambda \hat{j}+2 \hat{k} ; \vec{b}=\mu \hat{i}+\hat{j}-\hat{k}\) are orthogonal and \(|\overrightarrow{\mathbf{a}}|=|\overrightarrow{\mathbf{b}}|\), then \((\lambda, \mu)=\)

87963 If \(\vec{a}\) and \(\vec{b}\) are mutually perpendicular unit vectors, then \((3 \vec{a}+2 \vec{b}) \cdot(5 \vec{a}-6 \vec{b})=\)

87964 If \(\overrightarrow{\mathbf{a}}=2 \hat{\mathrm{i}}+\lambda \hat{\mathrm{j}}+\hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\) are orthogonal, then value of \(\lambda\) is

87965 Let \(\vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}\). If \(\vec{b}\) is a vector such that \(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathrm{b}}=|\overrightarrow{\mathrm{b}}|^2\) and \(|\overrightarrow{\mathbf{a}}-\overrightarrow{\mathrm{b}}|=\sqrt{7}\), then \(|\overrightarrow{\mathrm{b}}|=\)

87961 If \(|\vec{a}|=16,|\vec{b}|=4\), then \(\sqrt{|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2}=\)

87962 If \(\vec{a}=\hat{i}+\lambda \hat{j}+2 \hat{k} ; \vec{b}=\mu \hat{i}+\hat{j}-\hat{k}\) are orthogonal and \(|\overrightarrow{\mathbf{a}}|=|\overrightarrow{\mathbf{b}}|\), then \((\lambda, \mu)=\)

87963 If \(\vec{a}\) and \(\vec{b}\) are mutually perpendicular unit vectors, then \((3 \vec{a}+2 \vec{b}) \cdot(5 \vec{a}-6 \vec{b})=\)

87964 If \(\overrightarrow{\mathbf{a}}=2 \hat{\mathrm{i}}+\lambda \hat{\mathrm{j}}+\hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\) are orthogonal, then value of \(\lambda\) is

87965 Let \(\vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}\). If \(\vec{b}\) is a vector such that \(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathrm{b}}=|\overrightarrow{\mathrm{b}}|^2\) and \(|\overrightarrow{\mathbf{a}}-\overrightarrow{\mathrm{b}}|=\sqrt{7}\), then \(|\overrightarrow{\mathrm{b}}|=\)

87961 If \(|\vec{a}|=16,|\vec{b}|=4\), then \(\sqrt{|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2}=\)

87962 If \(\vec{a}=\hat{i}+\lambda \hat{j}+2 \hat{k} ; \vec{b}=\mu \hat{i}+\hat{j}-\hat{k}\) are orthogonal and \(|\overrightarrow{\mathbf{a}}|=|\overrightarrow{\mathbf{b}}|\), then \((\lambda, \mu)=\)

87963 If \(\vec{a}\) and \(\vec{b}\) are mutually perpendicular unit vectors, then \((3 \vec{a}+2 \vec{b}) \cdot(5 \vec{a}-6 \vec{b})=\)

87964 If \(\overrightarrow{\mathbf{a}}=2 \hat{\mathrm{i}}+\lambda \hat{\mathrm{j}}+\hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\) are orthogonal, then value of \(\lambda\) is

87965 Let \(\vec{a}=\hat{i}-2 \hat{j}+3 \hat{k}\). If \(\vec{b}\) is a vector such that \(\overrightarrow{\mathbf{a}} \cdot \overrightarrow{\mathrm{b}}=|\overrightarrow{\mathrm{b}}|^2\) and \(|\overrightarrow{\mathbf{a}}-\overrightarrow{\mathrm{b}}|=\sqrt{7}\), then \(|\overrightarrow{\mathrm{b}}|=\)