87686 The position vector of a point \(R\) which divides the line joining two points \(P\) and \(Q\) whose position vectors are \(\hat{i}+2 \hat{j}-\hat{k}\) and \(-\hat{i}+\hat{j}-\hat{k}\) respectively, in the ratio \(2: 1\) externally is

87687 The points having position vectors \(60 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}, 40 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}, \mathrm{a} \hat{\mathrm{i}}-52 \hat{\mathrm{j}}\), are collinear, if \(\mathrm{a}=\)

87688 The position vectors of \(A\) and \(B\) \(\operatorname{are}(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\) and \(\left(\frac{1}{3} \hat{\mathbf{j}}+\frac{1}{3} \hat{\mathbf{k}}\right)\). If 'B' divides the line \(A C\) in the ratio \(2: 1\), then position vector of ' \(C\) ' is

87689 The locus of a point which is at a distance of 4 units from \((3,-2)\) in xy-plane is \(\qquad\)

87686 The position vector of a point \(R\) which divides the line joining two points \(P\) and \(Q\) whose position vectors are \(\hat{i}+2 \hat{j}-\hat{k}\) and \(-\hat{i}+\hat{j}-\hat{k}\) respectively, in the ratio \(2: 1\) externally is

87687 The points having position vectors \(60 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}, 40 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}, \mathrm{a} \hat{\mathrm{i}}-52 \hat{\mathrm{j}}\), are collinear, if \(\mathrm{a}=\)

87688 The position vectors of \(A\) and \(B\) \(\operatorname{are}(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\) and \(\left(\frac{1}{3} \hat{\mathbf{j}}+\frac{1}{3} \hat{\mathbf{k}}\right)\). If 'B' divides the line \(A C\) in the ratio \(2: 1\), then position vector of ' \(C\) ' is

87689 The locus of a point which is at a distance of 4 units from \((3,-2)\) in xy-plane is \(\qquad\)

87686 The position vector of a point \(R\) which divides the line joining two points \(P\) and \(Q\) whose position vectors are \(\hat{i}+2 \hat{j}-\hat{k}\) and \(-\hat{i}+\hat{j}-\hat{k}\) respectively, in the ratio \(2: 1\) externally is

87687 The points having position vectors \(60 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}, 40 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}, \mathrm{a} \hat{\mathrm{i}}-52 \hat{\mathrm{j}}\), are collinear, if \(\mathrm{a}=\)

87688 The position vectors of \(A\) and \(B\) \(\operatorname{are}(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\) and \(\left(\frac{1}{3} \hat{\mathbf{j}}+\frac{1}{3} \hat{\mathbf{k}}\right)\). If 'B' divides the line \(A C\) in the ratio \(2: 1\), then position vector of ' \(C\) ' is

87689 The locus of a point which is at a distance of 4 units from \((3,-2)\) in xy-plane is \(\qquad\)

87686 The position vector of a point \(R\) which divides the line joining two points \(P\) and \(Q\) whose position vectors are \(\hat{i}+2 \hat{j}-\hat{k}\) and \(-\hat{i}+\hat{j}-\hat{k}\) respectively, in the ratio \(2: 1\) externally is

87687 The points having position vectors \(60 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}, 40 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}, \mathrm{a} \hat{\mathrm{i}}-52 \hat{\mathrm{j}}\), are collinear, if \(\mathrm{a}=\)

87688 The position vectors of \(A\) and \(B\) \(\operatorname{are}(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\) and \(\left(\frac{1}{3} \hat{\mathbf{j}}+\frac{1}{3} \hat{\mathbf{k}}\right)\). If 'B' divides the line \(A C\) in the ratio \(2: 1\), then position vector of ' \(C\) ' is

87689 The locus of a point which is at a distance of 4 units from \((3,-2)\) in xy-plane is \(\qquad\)