87813 If the position vectors of \(A, B, C\) are respectively \(\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}\) and \(2 \hat{\mathbf{i}}-\hat{\mathbf{k}}\), then the projection of \(A B\) on \(B C\) is equal to

87814 If the projection of \(\mathrm{PQ}\) on \(\mathrm{OX}, \mathrm{OY}, \mathrm{OZ}\) are respectively 12,3 and 4 , then the magnitude of \(P Q\) is

87815 Consider a tetrahedron with \(f\) aces \(\mathbf{F}_1, \mathbf{F}_2, \mathbf{F}_3, \mathbf{F}_4\) Let \(\overrightarrow{\mathbf{V}}_1, \overrightarrow{\mathbf{V}}_2, \overrightarrow{\mathbf{V}}_3, \overrightarrow{\mathbf{V}}_4\) be the vectors whose magnitudes are respectively equal to areas of \(F_1, F_2, F_3, F_4\) and whose directions are perpendicular to these faces in outward direction, then \(\left|\overrightarrow{\mathbf{V}}_1+\overrightarrow{\mathbf{V}}_2+\overrightarrow{\mathbf{V}}_3+\overrightarrow{\mathbf{V}}_4\right|\) equals

87816 In a trapezoid of the vector \(\overrightarrow{\mathrm{BC}}=\lambda \overrightarrow{\mathrm{AD}}\). We will, then find that \(\overrightarrow{\mathrm{P}}=\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{BD}}\) is collinear with \(\overrightarrow{\mathrm{AD}}\).If \(\overrightarrow{\mathrm{P}}=\mu \overrightarrow{\mathrm{AD}}\), then

87817 The area of a parallelogram with diagonals as \(\vec{a}=3 \hat{i}+\hat{j}-2 \hat{k}\) and \(\vec{b}=\hat{i}-3 \hat{j}+4 \hat{k}\) is

87813 If the position vectors of \(A, B, C\) are respectively \(\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}\) and \(2 \hat{\mathbf{i}}-\hat{\mathbf{k}}\), then the projection of \(A B\) on \(B C\) is equal to

87814 If the projection of \(\mathrm{PQ}\) on \(\mathrm{OX}, \mathrm{OY}, \mathrm{OZ}\) are respectively 12,3 and 4 , then the magnitude of \(P Q\) is

87815 Consider a tetrahedron with \(f\) aces \(\mathbf{F}_1, \mathbf{F}_2, \mathbf{F}_3, \mathbf{F}_4\) Let \(\overrightarrow{\mathbf{V}}_1, \overrightarrow{\mathbf{V}}_2, \overrightarrow{\mathbf{V}}_3, \overrightarrow{\mathbf{V}}_4\) be the vectors whose magnitudes are respectively equal to areas of \(F_1, F_2, F_3, F_4\) and whose directions are perpendicular to these faces in outward direction, then \(\left|\overrightarrow{\mathbf{V}}_1+\overrightarrow{\mathbf{V}}_2+\overrightarrow{\mathbf{V}}_3+\overrightarrow{\mathbf{V}}_4\right|\) equals

87816 In a trapezoid of the vector \(\overrightarrow{\mathrm{BC}}=\lambda \overrightarrow{\mathrm{AD}}\). We will, then find that \(\overrightarrow{\mathrm{P}}=\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{BD}}\) is collinear with \(\overrightarrow{\mathrm{AD}}\).If \(\overrightarrow{\mathrm{P}}=\mu \overrightarrow{\mathrm{AD}}\), then

87817 The area of a parallelogram with diagonals as \(\vec{a}=3 \hat{i}+\hat{j}-2 \hat{k}\) and \(\vec{b}=\hat{i}-3 \hat{j}+4 \hat{k}\) is

87813 If the position vectors of \(A, B, C\) are respectively \(\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}\) and \(2 \hat{\mathbf{i}}-\hat{\mathbf{k}}\), then the projection of \(A B\) on \(B C\) is equal to

87814 If the projection of \(\mathrm{PQ}\) on \(\mathrm{OX}, \mathrm{OY}, \mathrm{OZ}\) are respectively 12,3 and 4 , then the magnitude of \(P Q\) is

87815 Consider a tetrahedron with \(f\) aces \(\mathbf{F}_1, \mathbf{F}_2, \mathbf{F}_3, \mathbf{F}_4\) Let \(\overrightarrow{\mathbf{V}}_1, \overrightarrow{\mathbf{V}}_2, \overrightarrow{\mathbf{V}}_3, \overrightarrow{\mathbf{V}}_4\) be the vectors whose magnitudes are respectively equal to areas of \(F_1, F_2, F_3, F_4\) and whose directions are perpendicular to these faces in outward direction, then \(\left|\overrightarrow{\mathbf{V}}_1+\overrightarrow{\mathbf{V}}_2+\overrightarrow{\mathbf{V}}_3+\overrightarrow{\mathbf{V}}_4\right|\) equals

87816 In a trapezoid of the vector \(\overrightarrow{\mathrm{BC}}=\lambda \overrightarrow{\mathrm{AD}}\). We will, then find that \(\overrightarrow{\mathrm{P}}=\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{BD}}\) is collinear with \(\overrightarrow{\mathrm{AD}}\).If \(\overrightarrow{\mathrm{P}}=\mu \overrightarrow{\mathrm{AD}}\), then

87817 The area of a parallelogram with diagonals as \(\vec{a}=3 \hat{i}+\hat{j}-2 \hat{k}\) and \(\vec{b}=\hat{i}-3 \hat{j}+4 \hat{k}\) is

87813 If the position vectors of \(A, B, C\) are respectively \(\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}\) and \(2 \hat{\mathbf{i}}-\hat{\mathbf{k}}\), then the projection of \(A B\) on \(B C\) is equal to

87814 If the projection of \(\mathrm{PQ}\) on \(\mathrm{OX}, \mathrm{OY}, \mathrm{OZ}\) are respectively 12,3 and 4 , then the magnitude of \(P Q\) is

87815 Consider a tetrahedron with \(f\) aces \(\mathbf{F}_1, \mathbf{F}_2, \mathbf{F}_3, \mathbf{F}_4\) Let \(\overrightarrow{\mathbf{V}}_1, \overrightarrow{\mathbf{V}}_2, \overrightarrow{\mathbf{V}}_3, \overrightarrow{\mathbf{V}}_4\) be the vectors whose magnitudes are respectively equal to areas of \(F_1, F_2, F_3, F_4\) and whose directions are perpendicular to these faces in outward direction, then \(\left|\overrightarrow{\mathbf{V}}_1+\overrightarrow{\mathbf{V}}_2+\overrightarrow{\mathbf{V}}_3+\overrightarrow{\mathbf{V}}_4\right|\) equals

87816 In a trapezoid of the vector \(\overrightarrow{\mathrm{BC}}=\lambda \overrightarrow{\mathrm{AD}}\). We will, then find that \(\overrightarrow{\mathrm{P}}=\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{BD}}\) is collinear with \(\overrightarrow{\mathrm{AD}}\).If \(\overrightarrow{\mathrm{P}}=\mu \overrightarrow{\mathrm{AD}}\), then

87817 The area of a parallelogram with diagonals as \(\vec{a}=3 \hat{i}+\hat{j}-2 \hat{k}\) and \(\vec{b}=\hat{i}-3 \hat{j}+4 \hat{k}\) is

87813 If the position vectors of \(A, B, C\) are respectively \(\hat{\mathbf{i}}-\mathbf{2} \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{2} \hat{\mathbf{i}}+\mathbf{3} \hat{\mathbf{j}}\) and \(2 \hat{\mathbf{i}}-\hat{\mathbf{k}}\), then the projection of \(A B\) on \(B C\) is equal to

87814 If the projection of \(\mathrm{PQ}\) on \(\mathrm{OX}, \mathrm{OY}, \mathrm{OZ}\) are respectively 12,3 and 4 , then the magnitude of \(P Q\) is

87815 Consider a tetrahedron with \(f\) aces \(\mathbf{F}_1, \mathbf{F}_2, \mathbf{F}_3, \mathbf{F}_4\) Let \(\overrightarrow{\mathbf{V}}_1, \overrightarrow{\mathbf{V}}_2, \overrightarrow{\mathbf{V}}_3, \overrightarrow{\mathbf{V}}_4\) be the vectors whose magnitudes are respectively equal to areas of \(F_1, F_2, F_3, F_4\) and whose directions are perpendicular to these faces in outward direction, then \(\left|\overrightarrow{\mathbf{V}}_1+\overrightarrow{\mathbf{V}}_2+\overrightarrow{\mathbf{V}}_3+\overrightarrow{\mathbf{V}}_4\right|\) equals

87816 In a trapezoid of the vector \(\overrightarrow{\mathrm{BC}}=\lambda \overrightarrow{\mathrm{AD}}\). We will, then find that \(\overrightarrow{\mathrm{P}}=\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{BD}}\) is collinear with \(\overrightarrow{\mathrm{AD}}\).If \(\overrightarrow{\mathrm{P}}=\mu \overrightarrow{\mathrm{AD}}\), then

87817 The area of a parallelogram with diagonals as \(\vec{a}=3 \hat{i}+\hat{j}-2 \hat{k}\) and \(\vec{b}=\hat{i}-3 \hat{j}+4 \hat{k}\) is