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Given vector \(\vec{A}=2 \hat{i}+3 \hat{j}\), the angle between \(\vec{A}\) and \(y\) -axis is a. \(\tan ^{-1}(3 / 2)\) b. \(\tan ^{-1}(2 / 3)\) c. \(\sin ^{-1}(2 / 3)\) d. \(\cos ^{-1}(2 / 3)\)

Which of the following pairs of forces cannot be added to give a resultant force of \(4 \mathrm{~N}\) ? a. \(2 \mathrm{~N}\) and \(8 \mathrm{~N}\) b. \(2 \mathrm{~N}\) and \(2 \mathrm{~N}\) c. \(2 \mathrm{~N}\) and \(6 \mathrm{~N}\) d. \(2 \mathrm{~N}\) and \(4 \mathrm{~N}\)

The resultant of two vectors \(\vec{P}\) and \(\vec{Q}\) is \(\vec{R}\). If the magnitude of \(\vec{Q}\) is doubled, the new resultant vector becomes perpendicular to \(\vec{P} .\) Then, the magnitude of \(\vec{R}\) is equal to a. \(P+Q\) b. \(P\) c. \(P-Q\) d. \(Q\)

The sum of the magnitudes of two forces acting at a point is \(16 \mathrm{~N} .\) The resultant of these forces is perpendicular to the smaller force and has a magnitude of \(8 \mathrm{~N}\). If the smaller force is of magnitude \(x\), then the value of \(x\) is a. \(2 \mathrm{~N}\) b. \(4 \mathrm{~N}\) c. \(6 \mathrm{~N}\) d. \(7 \mathrm{~N}\)