87828 If \(a, b, c\) are unit vectors satisfying the relation \(a+b+\sqrt{3} c=0\), then the angle between \(a\) and \(b\) is

87810 If vectors \(a_1=x \hat{i}-\hat{j}+\hat{k}\) and \(a_2=\hat{i}+y \hat{j}+z \hat{k}\) are collinear, then a possible unit vector parallel to the vector \(x \hat{\mathbf{i}}+\mathbf{y} \hat{\mathbf{j}}+\mathbf{z} \hat{\mathbf{k}}\) is

87811 The magnitude of the projection of the vector \(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) on the vector perpendicular to the plane containing the vectors \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) is

87812 If \(\overrightarrow{\mathbf{a}}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}+\hat{j}+2 \hat{k}\) and \(\vec{c}=2 \hat{i}+3 \hat{j}-4 \hat{k}\) then the magnitude of the projection on \(\overrightarrow{\mathbf{c}}\) of \(\vec{a}\) unit vector that is perpendicular to both \(\vec{a}\) and \(\vec{b}\) is

87828 If \(a, b, c\) are unit vectors satisfying the relation \(a+b+\sqrt{3} c=0\), then the angle between \(a\) and \(b\) is

87810 If vectors \(a_1=x \hat{i}-\hat{j}+\hat{k}\) and \(a_2=\hat{i}+y \hat{j}+z \hat{k}\) are collinear, then a possible unit vector parallel to the vector \(x \hat{\mathbf{i}}+\mathbf{y} \hat{\mathbf{j}}+\mathbf{z} \hat{\mathbf{k}}\) is

87811 The magnitude of the projection of the vector \(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) on the vector perpendicular to the plane containing the vectors \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) is

87812 If \(\overrightarrow{\mathbf{a}}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}+\hat{j}+2 \hat{k}\) and \(\vec{c}=2 \hat{i}+3 \hat{j}-4 \hat{k}\) then the magnitude of the projection on \(\overrightarrow{\mathbf{c}}\) of \(\vec{a}\) unit vector that is perpendicular to both \(\vec{a}\) and \(\vec{b}\) is

87828 If \(a, b, c\) are unit vectors satisfying the relation \(a+b+\sqrt{3} c=0\), then the angle between \(a\) and \(b\) is

87810 If vectors \(a_1=x \hat{i}-\hat{j}+\hat{k}\) and \(a_2=\hat{i}+y \hat{j}+z \hat{k}\) are collinear, then a possible unit vector parallel to the vector \(x \hat{\mathbf{i}}+\mathbf{y} \hat{\mathbf{j}}+\mathbf{z} \hat{\mathbf{k}}\) is

87811 The magnitude of the projection of the vector \(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) on the vector perpendicular to the plane containing the vectors \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) is

87812 If \(\overrightarrow{\mathbf{a}}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}+\hat{j}+2 \hat{k}\) and \(\vec{c}=2 \hat{i}+3 \hat{j}-4 \hat{k}\) then the magnitude of the projection on \(\overrightarrow{\mathbf{c}}\) of \(\vec{a}\) unit vector that is perpendicular to both \(\vec{a}\) and \(\vec{b}\) is

87828 If \(a, b, c\) are unit vectors satisfying the relation \(a+b+\sqrt{3} c=0\), then the angle between \(a\) and \(b\) is

87810 If vectors \(a_1=x \hat{i}-\hat{j}+\hat{k}\) and \(a_2=\hat{i}+y \hat{j}+z \hat{k}\) are collinear, then a possible unit vector parallel to the vector \(x \hat{\mathbf{i}}+\mathbf{y} \hat{\mathbf{j}}+\mathbf{z} \hat{\mathbf{k}}\) is

87811 The magnitude of the projection of the vector \(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) on the vector perpendicular to the plane containing the vectors \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) is

87812 If \(\overrightarrow{\mathbf{a}}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}+\hat{j}+2 \hat{k}\) and \(\vec{c}=2 \hat{i}+3 \hat{j}-4 \hat{k}\) then the magnitude of the projection on \(\overrightarrow{\mathbf{c}}\) of \(\vec{a}\) unit vector that is perpendicular to both \(\vec{a}\) and \(\vec{b}\) is