87894 The vector \(\overrightarrow{\mathbf{x}}\) is perpendicular to the vectors \(\vec{a}=3 \hat{i}+2 \hat{j}+2 \hat{k}, \vec{b}=18 \hat{i}-22 \hat{j}-5 \hat{k}\) and makes an obtuse angle with \(\vec{j} \cdot\) If \(|x|=14\), then \(\overrightarrow{\mathbf{x}}=\)

87895 If \(\overrightarrow{\mathbf{c}}\) is the unit vector in the direction of sum of the vectors \(\vec{a}=2 \hat{i}+2 \hat{j}-5 \hat{k}\) and \(\vec{b}=2 \hat{i}+\hat{j}+3 \hat{k}\) then \(|\overrightarrow{\mathbf{c}}|=\) \(\qquad\)

87896 The direction angles of the line \(x=4 z+3, y=2\) \(-3 \mathrm{z}\) are \(\alpha, \beta\) and \(\gamma\) then \(\cos \alpha+\cos \beta+\cos \gamma=\ldots\).

87897 The angle between \(\vec{a}\) and \(\vec{b}\) is \(\frac{5 \pi}{6}\) and the projection of \(\vec{a}\) in the direction of \(\vec{b}\) is \(\frac{-6}{\sqrt{3}}\), then \(|\overrightarrow{\mathbf{a}}|\) is equal to:

87898 Equation of the plane that contains the lines \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\lambda(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}})\)
and \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\mu(-\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}})\), is

87894 The vector \(\overrightarrow{\mathbf{x}}\) is perpendicular to the vectors \(\vec{a}=3 \hat{i}+2 \hat{j}+2 \hat{k}, \vec{b}=18 \hat{i}-22 \hat{j}-5 \hat{k}\) and makes an obtuse angle with \(\vec{j} \cdot\) If \(|x|=14\), then \(\overrightarrow{\mathbf{x}}=\)

87895 If \(\overrightarrow{\mathbf{c}}\) is the unit vector in the direction of sum of the vectors \(\vec{a}=2 \hat{i}+2 \hat{j}-5 \hat{k}\) and \(\vec{b}=2 \hat{i}+\hat{j}+3 \hat{k}\) then \(|\overrightarrow{\mathbf{c}}|=\) \(\qquad\)

87896 The direction angles of the line \(x=4 z+3, y=2\) \(-3 \mathrm{z}\) are \(\alpha, \beta\) and \(\gamma\) then \(\cos \alpha+\cos \beta+\cos \gamma=\ldots\).

87897 The angle between \(\vec{a}\) and \(\vec{b}\) is \(\frac{5 \pi}{6}\) and the projection of \(\vec{a}\) in the direction of \(\vec{b}\) is \(\frac{-6}{\sqrt{3}}\), then \(|\overrightarrow{\mathbf{a}}|\) is equal to:

87898 Equation of the plane that contains the lines \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\lambda(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}})\)
and \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\mu(-\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}})\), is

87894 The vector \(\overrightarrow{\mathbf{x}}\) is perpendicular to the vectors \(\vec{a}=3 \hat{i}+2 \hat{j}+2 \hat{k}, \vec{b}=18 \hat{i}-22 \hat{j}-5 \hat{k}\) and makes an obtuse angle with \(\vec{j} \cdot\) If \(|x|=14\), then \(\overrightarrow{\mathbf{x}}=\)

87895 If \(\overrightarrow{\mathbf{c}}\) is the unit vector in the direction of sum of the vectors \(\vec{a}=2 \hat{i}+2 \hat{j}-5 \hat{k}\) and \(\vec{b}=2 \hat{i}+\hat{j}+3 \hat{k}\) then \(|\overrightarrow{\mathbf{c}}|=\) \(\qquad\)

87896 The direction angles of the line \(x=4 z+3, y=2\) \(-3 \mathrm{z}\) are \(\alpha, \beta\) and \(\gamma\) then \(\cos \alpha+\cos \beta+\cos \gamma=\ldots\).

87897 The angle between \(\vec{a}\) and \(\vec{b}\) is \(\frac{5 \pi}{6}\) and the projection of \(\vec{a}\) in the direction of \(\vec{b}\) is \(\frac{-6}{\sqrt{3}}\), then \(|\overrightarrow{\mathbf{a}}|\) is equal to:

87898 Equation of the plane that contains the lines \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\lambda(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}})\)
and \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\mu(-\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}})\), is

87894 The vector \(\overrightarrow{\mathbf{x}}\) is perpendicular to the vectors \(\vec{a}=3 \hat{i}+2 \hat{j}+2 \hat{k}, \vec{b}=18 \hat{i}-22 \hat{j}-5 \hat{k}\) and makes an obtuse angle with \(\vec{j} \cdot\) If \(|x|=14\), then \(\overrightarrow{\mathbf{x}}=\)

87895 If \(\overrightarrow{\mathbf{c}}\) is the unit vector in the direction of sum of the vectors \(\vec{a}=2 \hat{i}+2 \hat{j}-5 \hat{k}\) and \(\vec{b}=2 \hat{i}+\hat{j}+3 \hat{k}\) then \(|\overrightarrow{\mathbf{c}}|=\) \(\qquad\)

87896 The direction angles of the line \(x=4 z+3, y=2\) \(-3 \mathrm{z}\) are \(\alpha, \beta\) and \(\gamma\) then \(\cos \alpha+\cos \beta+\cos \gamma=\ldots\).

87897 The angle between \(\vec{a}\) and \(\vec{b}\) is \(\frac{5 \pi}{6}\) and the projection of \(\vec{a}\) in the direction of \(\vec{b}\) is \(\frac{-6}{\sqrt{3}}\), then \(|\overrightarrow{\mathbf{a}}|\) is equal to:

87898 Equation of the plane that contains the lines \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\lambda(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}})\)
and \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\mu(-\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}})\), is

87894 The vector \(\overrightarrow{\mathbf{x}}\) is perpendicular to the vectors \(\vec{a}=3 \hat{i}+2 \hat{j}+2 \hat{k}, \vec{b}=18 \hat{i}-22 \hat{j}-5 \hat{k}\) and makes an obtuse angle with \(\vec{j} \cdot\) If \(|x|=14\), then \(\overrightarrow{\mathbf{x}}=\)

87895 If \(\overrightarrow{\mathbf{c}}\) is the unit vector in the direction of sum of the vectors \(\vec{a}=2 \hat{i}+2 \hat{j}-5 \hat{k}\) and \(\vec{b}=2 \hat{i}+\hat{j}+3 \hat{k}\) then \(|\overrightarrow{\mathbf{c}}|=\) \(\qquad\)

87896 The direction angles of the line \(x=4 z+3, y=2\) \(-3 \mathrm{z}\) are \(\alpha, \beta\) and \(\gamma\) then \(\cos \alpha+\cos \beta+\cos \gamma=\ldots\).

87897 The angle between \(\vec{a}\) and \(\vec{b}\) is \(\frac{5 \pi}{6}\) and the projection of \(\vec{a}\) in the direction of \(\vec{b}\) is \(\frac{-6}{\sqrt{3}}\), then \(|\overrightarrow{\mathbf{a}}|\) is equal to:

87898 Equation of the plane that contains the lines \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\lambda(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}})\)
and \(\overrightarrow{\mathbf{r}}=(\hat{\mathbf{i}}+\hat{\mathbf{j}})+\mu(-\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}})\), is