121132 The direction cosine of a line which is perpendicular to both the lines whose direction ratios are \(-1,2,2\) and \(0,2,1\) are

121157 If \(A=(1,8,4), B=(2,-3,1)\), then the direction cosines of a normal to the plane \(A O B\) is

121181 Let \(6 x-3 y+2 z-6=0\) be the given plane. If a, \(b\) and \(c\) are the intercepts made by the plane on \(\mathrm{X}, \mathrm{Y}\) and \(\mathrm{Z}\)-axes, respectively; \(l, \mathrm{~m}\) and \(\mathrm{n}\) are the direction cosines of a normal drawn to the plane and \(p\) is the perpendicular distance from the origin to the plane, then \( \vert\mathbf{a} l+\mathrm{bm}+\mathbf{c n} \vert=\)

121122 If the line given by \(\overline{\mathbf{r}}=2 \hat{\mathbf{i}}+\lambda(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\mathrm{m} \hat{\mathbf{k}})\) and \(\overline{\mathbf{r}}=\hat{\mathbf{i}}+\mu(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+6 \hat{\mathbf{k}})\) are perpendicular, then the value of \(m\) is

121132 The direction cosine of a line which is perpendicular to both the lines whose direction ratios are \(-1,2,2\) and \(0,2,1\) are

121157 If \(A=(1,8,4), B=(2,-3,1)\), then the direction cosines of a normal to the plane \(A O B\) is

121181 Let \(6 x-3 y+2 z-6=0\) be the given plane. If a, \(b\) and \(c\) are the intercepts made by the plane on \(\mathrm{X}, \mathrm{Y}\) and \(\mathrm{Z}\)-axes, respectively; \(l, \mathrm{~m}\) and \(\mathrm{n}\) are the direction cosines of a normal drawn to the plane and \(p\) is the perpendicular distance from the origin to the plane, then \( \vert\mathbf{a} l+\mathrm{bm}+\mathbf{c n} \vert=\)

121122 If the line given by \(\overline{\mathbf{r}}=2 \hat{\mathbf{i}}+\lambda(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\mathrm{m} \hat{\mathbf{k}})\) and \(\overline{\mathbf{r}}=\hat{\mathbf{i}}+\mu(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+6 \hat{\mathbf{k}})\) are perpendicular, then the value of \(m\) is

121132 The direction cosine of a line which is perpendicular to both the lines whose direction ratios are \(-1,2,2\) and \(0,2,1\) are

121157 If \(A=(1,8,4), B=(2,-3,1)\), then the direction cosines of a normal to the plane \(A O B\) is

121181 Let \(6 x-3 y+2 z-6=0\) be the given plane. If a, \(b\) and \(c\) are the intercepts made by the plane on \(\mathrm{X}, \mathrm{Y}\) and \(\mathrm{Z}\)-axes, respectively; \(l, \mathrm{~m}\) and \(\mathrm{n}\) are the direction cosines of a normal drawn to the plane and \(p\) is the perpendicular distance from the origin to the plane, then \( \vert\mathbf{a} l+\mathrm{bm}+\mathbf{c n} \vert=\)

121122 If the line given by \(\overline{\mathbf{r}}=2 \hat{\mathbf{i}}+\lambda(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\mathrm{m} \hat{\mathbf{k}})\) and \(\overline{\mathbf{r}}=\hat{\mathbf{i}}+\mu(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+6 \hat{\mathbf{k}})\) are perpendicular, then the value of \(m\) is

121132 The direction cosine of a line which is perpendicular to both the lines whose direction ratios are \(-1,2,2\) and \(0,2,1\) are

121157 If \(A=(1,8,4), B=(2,-3,1)\), then the direction cosines of a normal to the plane \(A O B\) is

121181 Let \(6 x-3 y+2 z-6=0\) be the given plane. If a, \(b\) and \(c\) are the intercepts made by the plane on \(\mathrm{X}, \mathrm{Y}\) and \(\mathrm{Z}\)-axes, respectively; \(l, \mathrm{~m}\) and \(\mathrm{n}\) are the direction cosines of a normal drawn to the plane and \(p\) is the perpendicular distance from the origin to the plane, then \( \vert\mathbf{a} l+\mathrm{bm}+\mathbf{c n} \vert=\)

121122 If the line given by \(\overline{\mathbf{r}}=2 \hat{\mathbf{i}}+\lambda(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\mathrm{m} \hat{\mathbf{k}})\) and \(\overline{\mathbf{r}}=\hat{\mathbf{i}}+\mu(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+6 \hat{\mathbf{k}})\) are perpendicular, then the value of \(m\) is