87712 Let \(A(3 \hat{i}+\hat{j}-\hat{k})\) and \(B(13 \hat{i}-4 \hat{j}+9 \hat{k})\) be two points on a line \(L\). \(C\) and \(D\) be the points on \(L\) on either side of \(A\) at distance of 9 and 6 units respectively and \(C\) lies between \(A\) and \(B\). Then position vectors of \(C\) and \(D\) are respectively

87713 If the orthocentre of the triangle whose vertices are \(2 \hat{i}+3 \hat{j}+5 \hat{k}, 5 \hat{i}+2 \hat{j}+3 \hat{k}\) and \(3 \hat{i}+5 \hat{j}+2 \hat{k}\) is \(\mathbf{x}+\mathbf{y}+z \hat{k}\), then

87714 If \(P, Q, R\) are the mid-point of the sides \(A B, B C\) and \(C A\) of \(\triangle A B C\) respectively, then \(P C-B Q=\)

87715 The position vector of \(a\) point \(P\) is \(\mathbf{2} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{3} \hat{\mathbf{k}}\) and \(\mathbf{a}=-\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are two vectors which determine a plane \(\pi\). The equation of a line through \(P\) normal to \(b\) and lying on the plane \(\pi\) is

87712 Let \(A(3 \hat{i}+\hat{j}-\hat{k})\) and \(B(13 \hat{i}-4 \hat{j}+9 \hat{k})\) be two points on a line \(L\). \(C\) and \(D\) be the points on \(L\) on either side of \(A\) at distance of 9 and 6 units respectively and \(C\) lies between \(A\) and \(B\). Then position vectors of \(C\) and \(D\) are respectively

87713 If the orthocentre of the triangle whose vertices are \(2 \hat{i}+3 \hat{j}+5 \hat{k}, 5 \hat{i}+2 \hat{j}+3 \hat{k}\) and \(3 \hat{i}+5 \hat{j}+2 \hat{k}\) is \(\mathbf{x}+\mathbf{y}+z \hat{k}\), then

87714 If \(P, Q, R\) are the mid-point of the sides \(A B, B C\) and \(C A\) of \(\triangle A B C\) respectively, then \(P C-B Q=\)

87715 The position vector of \(a\) point \(P\) is \(\mathbf{2} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{3} \hat{\mathbf{k}}\) and \(\mathbf{a}=-\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are two vectors which determine a plane \(\pi\). The equation of a line through \(P\) normal to \(b\) and lying on the plane \(\pi\) is

87712 Let \(A(3 \hat{i}+\hat{j}-\hat{k})\) and \(B(13 \hat{i}-4 \hat{j}+9 \hat{k})\) be two points on a line \(L\). \(C\) and \(D\) be the points on \(L\) on either side of \(A\) at distance of 9 and 6 units respectively and \(C\) lies between \(A\) and \(B\). Then position vectors of \(C\) and \(D\) are respectively

87713 If the orthocentre of the triangle whose vertices are \(2 \hat{i}+3 \hat{j}+5 \hat{k}, 5 \hat{i}+2 \hat{j}+3 \hat{k}\) and \(3 \hat{i}+5 \hat{j}+2 \hat{k}\) is \(\mathbf{x}+\mathbf{y}+z \hat{k}\), then

87714 If \(P, Q, R\) are the mid-point of the sides \(A B, B C\) and \(C A\) of \(\triangle A B C\) respectively, then \(P C-B Q=\)

87715 The position vector of \(a\) point \(P\) is \(\mathbf{2} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{3} \hat{\mathbf{k}}\) and \(\mathbf{a}=-\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are two vectors which determine a plane \(\pi\). The equation of a line through \(P\) normal to \(b\) and lying on the plane \(\pi\) is

87712 Let \(A(3 \hat{i}+\hat{j}-\hat{k})\) and \(B(13 \hat{i}-4 \hat{j}+9 \hat{k})\) be two points on a line \(L\). \(C\) and \(D\) be the points on \(L\) on either side of \(A\) at distance of 9 and 6 units respectively and \(C\) lies between \(A\) and \(B\). Then position vectors of \(C\) and \(D\) are respectively

87713 If the orthocentre of the triangle whose vertices are \(2 \hat{i}+3 \hat{j}+5 \hat{k}, 5 \hat{i}+2 \hat{j}+3 \hat{k}\) and \(3 \hat{i}+5 \hat{j}+2 \hat{k}\) is \(\mathbf{x}+\mathbf{y}+z \hat{k}\), then

87714 If \(P, Q, R\) are the mid-point of the sides \(A B, B C\) and \(C A\) of \(\triangle A B C\) respectively, then \(P C-B Q=\)

87715 The position vector of \(a\) point \(P\) is \(\mathbf{2} \hat{\mathbf{i}}+\hat{\mathbf{j}}+\mathbf{3} \hat{\mathbf{k}}\) and \(\mathbf{a}=-\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) are two vectors which determine a plane \(\pi\). The equation of a line through \(P\) normal to \(b\) and lying on the plane \(\pi\) is