268984 Three forces \(\vec{F}_{1}=a(\hat{i}-\hat{j}+\hat{k}), \vec{F}_{2}=2 \hat{i}-3 \hat{j}+4 \hat{k}\) and \(\vec{F}_{3}=8 \hat{i}-7 \hat{j}+6 \hat{k}\) act simultaneously on a particle. If the particle is in equilibrium, the value of \(a\) is

268985 If a particle is displaced from \((0,0,0)\) to a point in XY - plane which is at a distance of 4 units in a direction making an angle clock wise \(60^{\circ}\) with the negative \(x\)-axis. What is the final position vector of the particle?

268986 Cosines of angles made by a vector with \(X, Y\) axes are \(3 / 5 \sqrt{2}, 4 / 5 \sqrt{2}\) respectively. If the magnitude of the vector is \(10 \sqrt{2}\) then that vector is

268987 If a vector \(\vec{A}\) makes angles \(45^{\circ}\) and \(60^{\circ}\) with \(x\) and \(y\) axis respectively then the angle made by it with \(\mathrm{z}\) - axis is

268988 A vector \(\vec{Q}\) which has a magnitude of 8 is added to the vector \(\vec{P}\) which lies along the \(\mathrm{X}\)-axis. The resultant of these two vectors is a third vector \(\vec{R}\) which lies along the \(\mathbf{Y}\)-axis and has a magnitude twice that of \(\vec{P}\). The magnitude of \(\vec{P}\) is

268984 Three forces \(\vec{F}_{1}=a(\hat{i}-\hat{j}+\hat{k}), \vec{F}_{2}=2 \hat{i}-3 \hat{j}+4 \hat{k}\) and \(\vec{F}_{3}=8 \hat{i}-7 \hat{j}+6 \hat{k}\) act simultaneously on a particle. If the particle is in equilibrium, the value of \(a\) is

268985 If a particle is displaced from \((0,0,0)\) to a point in XY - plane which is at a distance of 4 units in a direction making an angle clock wise \(60^{\circ}\) with the negative \(x\)-axis. What is the final position vector of the particle?

268986 Cosines of angles made by a vector with \(X, Y\) axes are \(3 / 5 \sqrt{2}, 4 / 5 \sqrt{2}\) respectively. If the magnitude of the vector is \(10 \sqrt{2}\) then that vector is

268987 If a vector \(\vec{A}\) makes angles \(45^{\circ}\) and \(60^{\circ}\) with \(x\) and \(y\) axis respectively then the angle made by it with \(\mathrm{z}\) - axis is

268988 A vector \(\vec{Q}\) which has a magnitude of 8 is added to the vector \(\vec{P}\) which lies along the \(\mathrm{X}\)-axis. The resultant of these two vectors is a third vector \(\vec{R}\) which lies along the \(\mathbf{Y}\)-axis and has a magnitude twice that of \(\vec{P}\). The magnitude of \(\vec{P}\) is

268984 Three forces \(\vec{F}_{1}=a(\hat{i}-\hat{j}+\hat{k}), \vec{F}_{2}=2 \hat{i}-3 \hat{j}+4 \hat{k}\) and \(\vec{F}_{3}=8 \hat{i}-7 \hat{j}+6 \hat{k}\) act simultaneously on a particle. If the particle is in equilibrium, the value of \(a\) is

268985 If a particle is displaced from \((0,0,0)\) to a point in XY - plane which is at a distance of 4 units in a direction making an angle clock wise \(60^{\circ}\) with the negative \(x\)-axis. What is the final position vector of the particle?

268986 Cosines of angles made by a vector with \(X, Y\) axes are \(3 / 5 \sqrt{2}, 4 / 5 \sqrt{2}\) respectively. If the magnitude of the vector is \(10 \sqrt{2}\) then that vector is

268987 If a vector \(\vec{A}\) makes angles \(45^{\circ}\) and \(60^{\circ}\) with \(x\) and \(y\) axis respectively then the angle made by it with \(\mathrm{z}\) - axis is

268988 A vector \(\vec{Q}\) which has a magnitude of 8 is added to the vector \(\vec{P}\) which lies along the \(\mathrm{X}\)-axis. The resultant of these two vectors is a third vector \(\vec{R}\) which lies along the \(\mathbf{Y}\)-axis and has a magnitude twice that of \(\vec{P}\). The magnitude of \(\vec{P}\) is

268984 Three forces \(\vec{F}_{1}=a(\hat{i}-\hat{j}+\hat{k}), \vec{F}_{2}=2 \hat{i}-3 \hat{j}+4 \hat{k}\) and \(\vec{F}_{3}=8 \hat{i}-7 \hat{j}+6 \hat{k}\) act simultaneously on a particle. If the particle is in equilibrium, the value of \(a\) is

268985 If a particle is displaced from \((0,0,0)\) to a point in XY - plane which is at a distance of 4 units in a direction making an angle clock wise \(60^{\circ}\) with the negative \(x\)-axis. What is the final position vector of the particle?

268986 Cosines of angles made by a vector with \(X, Y\) axes are \(3 / 5 \sqrt{2}, 4 / 5 \sqrt{2}\) respectively. If the magnitude of the vector is \(10 \sqrt{2}\) then that vector is

268987 If a vector \(\vec{A}\) makes angles \(45^{\circ}\) and \(60^{\circ}\) with \(x\) and \(y\) axis respectively then the angle made by it with \(\mathrm{z}\) - axis is

268988 A vector \(\vec{Q}\) which has a magnitude of 8 is added to the vector \(\vec{P}\) which lies along the \(\mathrm{X}\)-axis. The resultant of these two vectors is a third vector \(\vec{R}\) which lies along the \(\mathbf{Y}\)-axis and has a magnitude twice that of \(\vec{P}\). The magnitude of \(\vec{P}\) is

268984 Three forces \(\vec{F}_{1}=a(\hat{i}-\hat{j}+\hat{k}), \vec{F}_{2}=2 \hat{i}-3 \hat{j}+4 \hat{k}\) and \(\vec{F}_{3}=8 \hat{i}-7 \hat{j}+6 \hat{k}\) act simultaneously on a particle. If the particle is in equilibrium, the value of \(a\) is

268985 If a particle is displaced from \((0,0,0)\) to a point in XY - plane which is at a distance of 4 units in a direction making an angle clock wise \(60^{\circ}\) with the negative \(x\)-axis. What is the final position vector of the particle?

268986 Cosines of angles made by a vector with \(X, Y\) axes are \(3 / 5 \sqrt{2}, 4 / 5 \sqrt{2}\) respectively. If the magnitude of the vector is \(10 \sqrt{2}\) then that vector is

268987 If a vector \(\vec{A}\) makes angles \(45^{\circ}\) and \(60^{\circ}\) with \(x\) and \(y\) axis respectively then the angle made by it with \(\mathrm{z}\) - axis is

268988 A vector \(\vec{Q}\) which has a magnitude of 8 is added to the vector \(\vec{P}\) which lies along the \(\mathrm{X}\)-axis. The resultant of these two vectors is a third vector \(\vec{R}\) which lies along the \(\mathbf{Y}\)-axis and has a magnitude twice that of \(\vec{P}\). The magnitude of \(\vec{P}\) is