Vector Algebra PYQs - Last 10 Years

Forces A and B act at a point. The sum of their magnitudes is 50 N and the magnitude of their resultant is 20 N . If the resultant is at $90^{\circ}$ with the smaller force, the magnitudes of A and B , in N are

Which of the following statements is/are true?
(A) Three vectors not lying in a plane give zero resultant
(B) Three vectors lying in a plane can give zero resultant
(C) Two vectors of different magnitude can be combined to give a zero resul...

The square of resultant of two equal electric field vectors is three times their product. Angle between them is

If \(\alpha, \beta\) and \(\gamma\) are the angles between the vectors \(\overrightarrow{\mathrm{P}}, \overrightarrow{\mathrm{Q}}\), and \(\overrightarrow{\mathrm{R}}\) and \(\alpha=90^{\circ}\) as shown in figure. the product of $$(\vec{Q}...

The sides of a parallelogram are represented by vectors \(\vec{p}=5 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\vec{q}=3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\). Then, the area of the parallelogram is

The resultant of two forces acting at an angle of 120\(^\circ\) is 10 kg-W and is perpendicular to one of the forces. That force is

A particle starts moving from point (2, 10, 1). Displacement for the particle is \(8\widehat i - 2\widehat j + \widehat k\). The final coordinates of the particle is