88176 The equation of a plane passing through the intersection of two planes \(x+2 y-3 z+2=0\) and \(6 x+y+z+1=0\) and parallel to the line \(\mathbf{x}-\mathbf{1}=\mathbf{y}+\mathbf{2}=\mathbf{7}-\mathrm{z}\) is

88177 If the vectors \(x \hat{i}-3 \hat{j}+7 \hat{k}\) and \(\hat{i}+y \hat{j}-z \hat{k}\) collinear, then the value of \(\frac{xy^2}{z}\) is equal to

88178 If line joining points \(A\) and \(B\) having position vectors \(6 \vec{a}-\mathbf{4} \vec{b}+4 \vec{c}\) and \(-4 \vec{c}\) respectively, and the line joining the points \(C\) and \(D\) having position vectors \(-\vec{a}-2 \vec{b}-3 \vec{c}\) and \(\vec{a}+2 \vec{b}-5 \vec{c}\) intersect, then their point of intersection is

88179 If points \(P(4,5, x), Q(3, y, 4)\) and \(R(5,8,0)\) are collinear, then the value of \(x+y\) is

88176 The equation of a plane passing through the intersection of two planes \(x+2 y-3 z+2=0\) and \(6 x+y+z+1=0\) and parallel to the line \(\mathbf{x}-\mathbf{1}=\mathbf{y}+\mathbf{2}=\mathbf{7}-\mathrm{z}\) is

88177 If the vectors \(x \hat{i}-3 \hat{j}+7 \hat{k}\) and \(\hat{i}+y \hat{j}-z \hat{k}\) collinear, then the value of \(\frac{xy^2}{z}\) is equal to

88178 If line joining points \(A\) and \(B\) having position vectors \(6 \vec{a}-\mathbf{4} \vec{b}+4 \vec{c}\) and \(-4 \vec{c}\) respectively, and the line joining the points \(C\) and \(D\) having position vectors \(-\vec{a}-2 \vec{b}-3 \vec{c}\) and \(\vec{a}+2 \vec{b}-5 \vec{c}\) intersect, then their point of intersection is

88179 If points \(P(4,5, x), Q(3, y, 4)\) and \(R(5,8,0)\) are collinear, then the value of \(x+y\) is

88176 The equation of a plane passing through the intersection of two planes \(x+2 y-3 z+2=0\) and \(6 x+y+z+1=0\) and parallel to the line \(\mathbf{x}-\mathbf{1}=\mathbf{y}+\mathbf{2}=\mathbf{7}-\mathrm{z}\) is

88177 If the vectors \(x \hat{i}-3 \hat{j}+7 \hat{k}\) and \(\hat{i}+y \hat{j}-z \hat{k}\) collinear, then the value of \(\frac{xy^2}{z}\) is equal to

88178 If line joining points \(A\) and \(B\) having position vectors \(6 \vec{a}-\mathbf{4} \vec{b}+4 \vec{c}\) and \(-4 \vec{c}\) respectively, and the line joining the points \(C\) and \(D\) having position vectors \(-\vec{a}-2 \vec{b}-3 \vec{c}\) and \(\vec{a}+2 \vec{b}-5 \vec{c}\) intersect, then their point of intersection is

88179 If points \(P(4,5, x), Q(3, y, 4)\) and \(R(5,8,0)\) are collinear, then the value of \(x+y\) is

88176 The equation of a plane passing through the intersection of two planes \(x+2 y-3 z+2=0\) and \(6 x+y+z+1=0\) and parallel to the line \(\mathbf{x}-\mathbf{1}=\mathbf{y}+\mathbf{2}=\mathbf{7}-\mathrm{z}\) is

88177 If the vectors \(x \hat{i}-3 \hat{j}+7 \hat{k}\) and \(\hat{i}+y \hat{j}-z \hat{k}\) collinear, then the value of \(\frac{xy^2}{z}\) is equal to

88178 If line joining points \(A\) and \(B\) having position vectors \(6 \vec{a}-\mathbf{4} \vec{b}+4 \vec{c}\) and \(-4 \vec{c}\) respectively, and the line joining the points \(C\) and \(D\) having position vectors \(-\vec{a}-2 \vec{b}-3 \vec{c}\) and \(\vec{a}+2 \vec{b}-5 \vec{c}\) intersect, then their point of intersection is

88179 If points \(P(4,5, x), Q(3, y, 4)\) and \(R(5,8,0)\) are collinear, then the value of \(x+y\) is