87667 If \(\overrightarrow{\mathrm{AB}}=3 \hat{\mathrm{i}}+5 \hat{\mathbf{j}}+4 \hat{\mathrm{k}}, \overrightarrow{\mathrm{AC}}=5 \hat{\mathrm{i}}-5 \hat{\mathbf{j}}+2 \hat{\mathrm{k}}\) represent the sides of triangle \(A B C\), then the length of median through \(A\) is

87668 If \(\vec{a}, \vec{b}, \vec{c}, \vec{d}\) are the position vector of the points
A, B, C, D respectively such that \(3 \vec{a}-\vec{b}+2 \vec{c}-4 \vec{d}=\overrightarrow{0}\), then the position vector of the point of intersection of the line segments \(A C\) and \(B D\) is

87669 If \(\vec{a}, \vec{b}, \vec{c}\) are the position vectors of the points \(A(1,3,0), B(2,5,0), C(4,2,0)\) respectively and \(\vec{c}=t_1 \vec{a}+t_2 \vec{b}\), then value of \(t_1 t_2=\)

87670 \(A \equiv(2,3,-2)\) and \(B \equiv(4,1,-2)\) are two vertices of \(\triangle A B C . P, Q\) and \(R\) are the midpoints of \(A B\), \(B C\) and \(A C\) respectively. The coordinates of \(R\) are \(\left(\frac{5}{2}, \frac{5}{2},-\frac{7}{2}\right)\). Then the centroid of \(\triangle P Q R\) is

87667 If \(\overrightarrow{\mathrm{AB}}=3 \hat{\mathrm{i}}+5 \hat{\mathbf{j}}+4 \hat{\mathrm{k}}, \overrightarrow{\mathrm{AC}}=5 \hat{\mathrm{i}}-5 \hat{\mathbf{j}}+2 \hat{\mathrm{k}}\) represent the sides of triangle \(A B C\), then the length of median through \(A\) is

87668 If \(\vec{a}, \vec{b}, \vec{c}, \vec{d}\) are the position vector of the points
A, B, C, D respectively such that \(3 \vec{a}-\vec{b}+2 \vec{c}-4 \vec{d}=\overrightarrow{0}\), then the position vector of the point of intersection of the line segments \(A C\) and \(B D\) is

87669 If \(\vec{a}, \vec{b}, \vec{c}\) are the position vectors of the points \(A(1,3,0), B(2,5,0), C(4,2,0)\) respectively and \(\vec{c}=t_1 \vec{a}+t_2 \vec{b}\), then value of \(t_1 t_2=\)

87670 \(A \equiv(2,3,-2)\) and \(B \equiv(4,1,-2)\) are two vertices of \(\triangle A B C . P, Q\) and \(R\) are the midpoints of \(A B\), \(B C\) and \(A C\) respectively. The coordinates of \(R\) are \(\left(\frac{5}{2}, \frac{5}{2},-\frac{7}{2}\right)\). Then the centroid of \(\triangle P Q R\) is

87667 If \(\overrightarrow{\mathrm{AB}}=3 \hat{\mathrm{i}}+5 \hat{\mathbf{j}}+4 \hat{\mathrm{k}}, \overrightarrow{\mathrm{AC}}=5 \hat{\mathrm{i}}-5 \hat{\mathbf{j}}+2 \hat{\mathrm{k}}\) represent the sides of triangle \(A B C\), then the length of median through \(A\) is

87668 If \(\vec{a}, \vec{b}, \vec{c}, \vec{d}\) are the position vector of the points
A, B, C, D respectively such that \(3 \vec{a}-\vec{b}+2 \vec{c}-4 \vec{d}=\overrightarrow{0}\), then the position vector of the point of intersection of the line segments \(A C\) and \(B D\) is

87669 If \(\vec{a}, \vec{b}, \vec{c}\) are the position vectors of the points \(A(1,3,0), B(2,5,0), C(4,2,0)\) respectively and \(\vec{c}=t_1 \vec{a}+t_2 \vec{b}\), then value of \(t_1 t_2=\)

87670 \(A \equiv(2,3,-2)\) and \(B \equiv(4,1,-2)\) are two vertices of \(\triangle A B C . P, Q\) and \(R\) are the midpoints of \(A B\), \(B C\) and \(A C\) respectively. The coordinates of \(R\) are \(\left(\frac{5}{2}, \frac{5}{2},-\frac{7}{2}\right)\). Then the centroid of \(\triangle P Q R\) is

87667 If \(\overrightarrow{\mathrm{AB}}=3 \hat{\mathrm{i}}+5 \hat{\mathbf{j}}+4 \hat{\mathrm{k}}, \overrightarrow{\mathrm{AC}}=5 \hat{\mathrm{i}}-5 \hat{\mathbf{j}}+2 \hat{\mathrm{k}}\) represent the sides of triangle \(A B C\), then the length of median through \(A\) is

87668 If \(\vec{a}, \vec{b}, \vec{c}, \vec{d}\) are the position vector of the points
A, B, C, D respectively such that \(3 \vec{a}-\vec{b}+2 \vec{c}-4 \vec{d}=\overrightarrow{0}\), then the position vector of the point of intersection of the line segments \(A C\) and \(B D\) is

87669 If \(\vec{a}, \vec{b}, \vec{c}\) are the position vectors of the points \(A(1,3,0), B(2,5,0), C(4,2,0)\) respectively and \(\vec{c}=t_1 \vec{a}+t_2 \vec{b}\), then value of \(t_1 t_2=\)

87670 \(A \equiv(2,3,-2)\) and \(B \equiv(4,1,-2)\) are two vertices of \(\triangle A B C . P, Q\) and \(R\) are the midpoints of \(A B\), \(B C\) and \(A C\) respectively. The coordinates of \(R\) are \(\left(\frac{5}{2}, \frac{5}{2},-\frac{7}{2}\right)\). Then the centroid of \(\triangle P Q R\) is