87870 The direction ratio of a line which is perpendicular to the line having direction ratio \(3,-2,1\) and \(1,2-1\) are

87871 If \(\vec{a}, \vec{b}, \vec{c}\), are mutually perpendicular unit vectors, then \(|\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}|\) is equal to :

87874 Let \(\vec{\alpha}=4 \hat{i}+3 \hat{j}+5 \hat{k}\) and \(\vec{\beta}=\hat{i}+2 \hat{j}-4 \hat{k}\). Let \(\vec{\beta}_1\) be parallel to \(\vec{\alpha}\) and \(\vec{\beta}_2\) be perpendicular to \(\vec{\alpha}\). If \(\vec{\beta}=\vec{\beta}_1+\vec{\beta}_2\), then the value of \(\mathbf{5} \overrightarrow{\boldsymbol{\beta}}_2(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\) is.

87876 The vectors \(3 a-5 b\) and \(2 a+b\) are mutually perpendicular and the vectors \(a+4 b\) and \(-\mathbf{a}+\mathbf{b}\) are also mutually perpendicular then the acute angle between \(a\) and \(b\) is

87877 a, b and \(c\) are three unit vectors such that no two of them are collinear. If \(\mathbf{b}=\mathbf{2}\{\mathbf{a} \times(\mathbf{b} \times \mathbf{c})\}\) and \(\alpha\) is the angle between \(a, c\) and \(\beta\) is the angle between \(a, b\) then \(\cos (\boldsymbol{\alpha}+\boldsymbol{\beta})=\)

87870 The direction ratio of a line which is perpendicular to the line having direction ratio \(3,-2,1\) and \(1,2-1\) are

87871 If \(\vec{a}, \vec{b}, \vec{c}\), are mutually perpendicular unit vectors, then \(|\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}|\) is equal to :

87874 Let \(\vec{\alpha}=4 \hat{i}+3 \hat{j}+5 \hat{k}\) and \(\vec{\beta}=\hat{i}+2 \hat{j}-4 \hat{k}\). Let \(\vec{\beta}_1\) be parallel to \(\vec{\alpha}\) and \(\vec{\beta}_2\) be perpendicular to \(\vec{\alpha}\). If \(\vec{\beta}=\vec{\beta}_1+\vec{\beta}_2\), then the value of \(\mathbf{5} \overrightarrow{\boldsymbol{\beta}}_2(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\) is.

87876 The vectors \(3 a-5 b\) and \(2 a+b\) are mutually perpendicular and the vectors \(a+4 b\) and \(-\mathbf{a}+\mathbf{b}\) are also mutually perpendicular then the acute angle between \(a\) and \(b\) is

87877 a, b and \(c\) are three unit vectors such that no two of them are collinear. If \(\mathbf{b}=\mathbf{2}\{\mathbf{a} \times(\mathbf{b} \times \mathbf{c})\}\) and \(\alpha\) is the angle between \(a, c\) and \(\beta\) is the angle between \(a, b\) then \(\cos (\boldsymbol{\alpha}+\boldsymbol{\beta})=\)

87870 The direction ratio of a line which is perpendicular to the line having direction ratio \(3,-2,1\) and \(1,2-1\) are

87871 If \(\vec{a}, \vec{b}, \vec{c}\), are mutually perpendicular unit vectors, then \(|\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}|\) is equal to :

87874 Let \(\vec{\alpha}=4 \hat{i}+3 \hat{j}+5 \hat{k}\) and \(\vec{\beta}=\hat{i}+2 \hat{j}-4 \hat{k}\). Let \(\vec{\beta}_1\) be parallel to \(\vec{\alpha}\) and \(\vec{\beta}_2\) be perpendicular to \(\vec{\alpha}\). If \(\vec{\beta}=\vec{\beta}_1+\vec{\beta}_2\), then the value of \(\mathbf{5} \overrightarrow{\boldsymbol{\beta}}_2(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\) is.

87876 The vectors \(3 a-5 b\) and \(2 a+b\) are mutually perpendicular and the vectors \(a+4 b\) and \(-\mathbf{a}+\mathbf{b}\) are also mutually perpendicular then the acute angle between \(a\) and \(b\) is

87877 a, b and \(c\) are three unit vectors such that no two of them are collinear. If \(\mathbf{b}=\mathbf{2}\{\mathbf{a} \times(\mathbf{b} \times \mathbf{c})\}\) and \(\alpha\) is the angle between \(a, c\) and \(\beta\) is the angle between \(a, b\) then \(\cos (\boldsymbol{\alpha}+\boldsymbol{\beta})=\)

87870 The direction ratio of a line which is perpendicular to the line having direction ratio \(3,-2,1\) and \(1,2-1\) are

87871 If \(\vec{a}, \vec{b}, \vec{c}\), are mutually perpendicular unit vectors, then \(|\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}|\) is equal to :

87874 Let \(\vec{\alpha}=4 \hat{i}+3 \hat{j}+5 \hat{k}\) and \(\vec{\beta}=\hat{i}+2 \hat{j}-4 \hat{k}\). Let \(\vec{\beta}_1\) be parallel to \(\vec{\alpha}\) and \(\vec{\beta}_2\) be perpendicular to \(\vec{\alpha}\). If \(\vec{\beta}=\vec{\beta}_1+\vec{\beta}_2\), then the value of \(\mathbf{5} \overrightarrow{\boldsymbol{\beta}}_2(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\) is.

87876 The vectors \(3 a-5 b\) and \(2 a+b\) are mutually perpendicular and the vectors \(a+4 b\) and \(-\mathbf{a}+\mathbf{b}\) are also mutually perpendicular then the acute angle between \(a\) and \(b\) is

87877 a, b and \(c\) are three unit vectors such that no two of them are collinear. If \(\mathbf{b}=\mathbf{2}\{\mathbf{a} \times(\mathbf{b} \times \mathbf{c})\}\) and \(\alpha\) is the angle between \(a, c\) and \(\beta\) is the angle between \(a, b\) then \(\cos (\boldsymbol{\alpha}+\boldsymbol{\beta})=\)

87870 The direction ratio of a line which is perpendicular to the line having direction ratio \(3,-2,1\) and \(1,2-1\) are

87871 If \(\vec{a}, \vec{b}, \vec{c}\), are mutually perpendicular unit vectors, then \(|\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}+\overrightarrow{\mathbf{c}}|\) is equal to :

87874 Let \(\vec{\alpha}=4 \hat{i}+3 \hat{j}+5 \hat{k}\) and \(\vec{\beta}=\hat{i}+2 \hat{j}-4 \hat{k}\). Let \(\vec{\beta}_1\) be parallel to \(\vec{\alpha}\) and \(\vec{\beta}_2\) be perpendicular to \(\vec{\alpha}\). If \(\vec{\beta}=\vec{\beta}_1+\vec{\beta}_2\), then the value of \(\mathbf{5} \overrightarrow{\boldsymbol{\beta}}_2(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\) is.

87876 The vectors \(3 a-5 b\) and \(2 a+b\) are mutually perpendicular and the vectors \(a+4 b\) and \(-\mathbf{a}+\mathbf{b}\) are also mutually perpendicular then the acute angle between \(a\) and \(b\) is

87877 a, b and \(c\) are three unit vectors such that no two of them are collinear. If \(\mathbf{b}=\mathbf{2}\{\mathbf{a} \times(\mathbf{b} \times \mathbf{c})\}\) and \(\alpha\) is the angle between \(a, c\) and \(\beta\) is the angle between \(a, b\) then \(\cos (\boldsymbol{\alpha}+\boldsymbol{\beta})=\)