87772 A vector \(\overrightarrow{\mathbf{a}}\) has components \(2 \mathrm{p}\) and 1 with respect to a rectangular Cartesian system. The system is rotated through a certain angle about the origin in the counter clockwise sense. If \(\vec{a}\) has components \(p+1\) and 1 with respect to the new system, then

87773 If the sum of two unit vectors is again a unit vector, then magnitude of their difference is

87774 Let \(O\) be the origin and the position vector of the point \(P\) be \(-\hat{i}-2 \hat{j}+3 \hat{k}\). If the position vectors of the points \(A, B\) and \(C\) are \(-2 \hat{i}+\hat{j}-3 \hat{k}, \quad 2 \hat{i}+4 \hat{j}-2 \hat{k}\) and \(-4 \hat{i}+2 \hat{j}-\hat{k}\) respectively then the projection of the vector \(\overline{\mathrm{OP}}\) on a vector perpendicular to the vectors \(\overrightarrow{\mathrm{AB}}\) and \(\overrightarrow{\mathrm{AC}}\) is

87775 Let \(\vec{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k} a_i>0, i=1,2,3\) be \(a\) vector which makes equal angles with the coordinates axes \(O X, O Y\) and \(O Z\). Also, let the projection of \(\vec{a}\) on the vector \(3 \hat{i}+4 \hat{j}\) be 7 . Let \(\vec{b}\) be a vector obtained by rotating \(\vec{a}\) with \(90^{\circ}\). If \(\vec{a}, \vec{b}\) and \(x\)-axis are coplanar, then projection of a vector \(\vec{b}\) on \(3 \hat{i}+4 \hat{j}\) is equal to

87772 A vector \(\overrightarrow{\mathbf{a}}\) has components \(2 \mathrm{p}\) and 1 with respect to a rectangular Cartesian system. The system is rotated through a certain angle about the origin in the counter clockwise sense. If \(\vec{a}\) has components \(p+1\) and 1 with respect to the new system, then

87773 If the sum of two unit vectors is again a unit vector, then magnitude of their difference is

87774 Let \(O\) be the origin and the position vector of the point \(P\) be \(-\hat{i}-2 \hat{j}+3 \hat{k}\). If the position vectors of the points \(A, B\) and \(C\) are \(-2 \hat{i}+\hat{j}-3 \hat{k}, \quad 2 \hat{i}+4 \hat{j}-2 \hat{k}\) and \(-4 \hat{i}+2 \hat{j}-\hat{k}\) respectively then the projection of the vector \(\overline{\mathrm{OP}}\) on a vector perpendicular to the vectors \(\overrightarrow{\mathrm{AB}}\) and \(\overrightarrow{\mathrm{AC}}\) is

87775 Let \(\vec{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k} a_i>0, i=1,2,3\) be \(a\) vector which makes equal angles with the coordinates axes \(O X, O Y\) and \(O Z\). Also, let the projection of \(\vec{a}\) on the vector \(3 \hat{i}+4 \hat{j}\) be 7 . Let \(\vec{b}\) be a vector obtained by rotating \(\vec{a}\) with \(90^{\circ}\). If \(\vec{a}, \vec{b}\) and \(x\)-axis are coplanar, then projection of a vector \(\vec{b}\) on \(3 \hat{i}+4 \hat{j}\) is equal to

87772 A vector \(\overrightarrow{\mathbf{a}}\) has components \(2 \mathrm{p}\) and 1 with respect to a rectangular Cartesian system. The system is rotated through a certain angle about the origin in the counter clockwise sense. If \(\vec{a}\) has components \(p+1\) and 1 with respect to the new system, then

87773 If the sum of two unit vectors is again a unit vector, then magnitude of their difference is

87774 Let \(O\) be the origin and the position vector of the point \(P\) be \(-\hat{i}-2 \hat{j}+3 \hat{k}\). If the position vectors of the points \(A, B\) and \(C\) are \(-2 \hat{i}+\hat{j}-3 \hat{k}, \quad 2 \hat{i}+4 \hat{j}-2 \hat{k}\) and \(-4 \hat{i}+2 \hat{j}-\hat{k}\) respectively then the projection of the vector \(\overline{\mathrm{OP}}\) on a vector perpendicular to the vectors \(\overrightarrow{\mathrm{AB}}\) and \(\overrightarrow{\mathrm{AC}}\) is

87775 Let \(\vec{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k} a_i>0, i=1,2,3\) be \(a\) vector which makes equal angles with the coordinates axes \(O X, O Y\) and \(O Z\). Also, let the projection of \(\vec{a}\) on the vector \(3 \hat{i}+4 \hat{j}\) be 7 . Let \(\vec{b}\) be a vector obtained by rotating \(\vec{a}\) with \(90^{\circ}\). If \(\vec{a}, \vec{b}\) and \(x\)-axis are coplanar, then projection of a vector \(\vec{b}\) on \(3 \hat{i}+4 \hat{j}\) is equal to

87772 A vector \(\overrightarrow{\mathbf{a}}\) has components \(2 \mathrm{p}\) and 1 with respect to a rectangular Cartesian system. The system is rotated through a certain angle about the origin in the counter clockwise sense. If \(\vec{a}\) has components \(p+1\) and 1 with respect to the new system, then

87773 If the sum of two unit vectors is again a unit vector, then magnitude of their difference is

87774 Let \(O\) be the origin and the position vector of the point \(P\) be \(-\hat{i}-2 \hat{j}+3 \hat{k}\). If the position vectors of the points \(A, B\) and \(C\) are \(-2 \hat{i}+\hat{j}-3 \hat{k}, \quad 2 \hat{i}+4 \hat{j}-2 \hat{k}\) and \(-4 \hat{i}+2 \hat{j}-\hat{k}\) respectively then the projection of the vector \(\overline{\mathrm{OP}}\) on a vector perpendicular to the vectors \(\overrightarrow{\mathrm{AB}}\) and \(\overrightarrow{\mathrm{AC}}\) is

87775 Let \(\vec{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k} a_i>0, i=1,2,3\) be \(a\) vector which makes equal angles with the coordinates axes \(O X, O Y\) and \(O Z\). Also, let the projection of \(\vec{a}\) on the vector \(3 \hat{i}+4 \hat{j}\) be 7 . Let \(\vec{b}\) be a vector obtained by rotating \(\vec{a}\) with \(90^{\circ}\). If \(\vec{a}, \vec{b}\) and \(x\)-axis are coplanar, then projection of a vector \(\vec{b}\) on \(3 \hat{i}+4 \hat{j}\) is equal to