88194 If \(P(3,2,-4), Q(9,8,-10)\) and \(R(5,4,-6)\) are collinear, then the ratio in which \(R\) divides \(P Q\) is

88195 The point if intersection of the lines
\(l_1: \mathbf{r}(\mathbf{t})=(\mathbf{I}-6 \mathbf{j}+\mathbf{2 k})+\mathbf{t}(\mathbf{i}+\mathbf{2} \mathbf{j}+\mathbf{k})\)
\(l_2: \mathbf{R}(\mathbf{u})=(\mathbf{4} \mathbf{j}+\mathbf{k})+\mathbf{u}(2 \mathbf{i}+\mathbf{j}+\mathbf{2 k}) \text { is }\)

88196 For scalars \(\lambda, \mu\) if the vector equation of a plane is
\(\mathbf{r}=(2-3 \lambda-\mu) \hat{\mathbf{i}}+(1-2 \lambda+3 \mu) \hat{\mathbf{j}}+(-2+2 \lambda+\mu) \hat{\mathbf{k}} \text {, }\)
then its Cartesian equation is

88197 If \(b, c\) are non collinear vectors, \(|c| \neq 0, a \times(b \times\)
c) \(+(\mathbf{a} . b) b=(4-2 \beta-\sin \alpha) b+\left(\beta^2-1\right) c\) and (c.c) \(\mathrm{a}=\mathrm{c}\), then the scalars \(\alpha\) and \(\beta\) are

88194 If \(P(3,2,-4), Q(9,8,-10)\) and \(R(5,4,-6)\) are collinear, then the ratio in which \(R\) divides \(P Q\) is

88195 The point if intersection of the lines
\(l_1: \mathbf{r}(\mathbf{t})=(\mathbf{I}-6 \mathbf{j}+\mathbf{2 k})+\mathbf{t}(\mathbf{i}+\mathbf{2} \mathbf{j}+\mathbf{k})\)
\(l_2: \mathbf{R}(\mathbf{u})=(\mathbf{4} \mathbf{j}+\mathbf{k})+\mathbf{u}(2 \mathbf{i}+\mathbf{j}+\mathbf{2 k}) \text { is }\)

88196 For scalars \(\lambda, \mu\) if the vector equation of a plane is
\(\mathbf{r}=(2-3 \lambda-\mu) \hat{\mathbf{i}}+(1-2 \lambda+3 \mu) \hat{\mathbf{j}}+(-2+2 \lambda+\mu) \hat{\mathbf{k}} \text {, }\)
then its Cartesian equation is

88197 If \(b, c\) are non collinear vectors, \(|c| \neq 0, a \times(b \times\)
c) \(+(\mathbf{a} . b) b=(4-2 \beta-\sin \alpha) b+\left(\beta^2-1\right) c\) and (c.c) \(\mathrm{a}=\mathrm{c}\), then the scalars \(\alpha\) and \(\beta\) are

88194 If \(P(3,2,-4), Q(9,8,-10)\) and \(R(5,4,-6)\) are collinear, then the ratio in which \(R\) divides \(P Q\) is

88195 The point if intersection of the lines
\(l_1: \mathbf{r}(\mathbf{t})=(\mathbf{I}-6 \mathbf{j}+\mathbf{2 k})+\mathbf{t}(\mathbf{i}+\mathbf{2} \mathbf{j}+\mathbf{k})\)
\(l_2: \mathbf{R}(\mathbf{u})=(\mathbf{4} \mathbf{j}+\mathbf{k})+\mathbf{u}(2 \mathbf{i}+\mathbf{j}+\mathbf{2 k}) \text { is }\)

88196 For scalars \(\lambda, \mu\) if the vector equation of a plane is
\(\mathbf{r}=(2-3 \lambda-\mu) \hat{\mathbf{i}}+(1-2 \lambda+3 \mu) \hat{\mathbf{j}}+(-2+2 \lambda+\mu) \hat{\mathbf{k}} \text {, }\)
then its Cartesian equation is

88197 If \(b, c\) are non collinear vectors, \(|c| \neq 0, a \times(b \times\)
c) \(+(\mathbf{a} . b) b=(4-2 \beta-\sin \alpha) b+\left(\beta^2-1\right) c\) and (c.c) \(\mathrm{a}=\mathrm{c}\), then the scalars \(\alpha\) and \(\beta\) are

88194 If \(P(3,2,-4), Q(9,8,-10)\) and \(R(5,4,-6)\) are collinear, then the ratio in which \(R\) divides \(P Q\) is

88195 The point if intersection of the lines
\(l_1: \mathbf{r}(\mathbf{t})=(\mathbf{I}-6 \mathbf{j}+\mathbf{2 k})+\mathbf{t}(\mathbf{i}+\mathbf{2} \mathbf{j}+\mathbf{k})\)
\(l_2: \mathbf{R}(\mathbf{u})=(\mathbf{4} \mathbf{j}+\mathbf{k})+\mathbf{u}(2 \mathbf{i}+\mathbf{j}+\mathbf{2 k}) \text { is }\)

88196 For scalars \(\lambda, \mu\) if the vector equation of a plane is
\(\mathbf{r}=(2-3 \lambda-\mu) \hat{\mathbf{i}}+(1-2 \lambda+3 \mu) \hat{\mathbf{j}}+(-2+2 \lambda+\mu) \hat{\mathbf{k}} \text {, }\)
then its Cartesian equation is

88197 If \(b, c\) are non collinear vectors, \(|c| \neq 0, a \times(b \times\)
c) \(+(\mathbf{a} . b) b=(4-2 \beta-\sin \alpha) b+\left(\beta^2-1\right) c\) and (c.c) \(\mathrm{a}=\mathrm{c}\), then the scalars \(\alpha\) and \(\beta\) are