00. Scalar and Vector Quantities
Motion in Plane

143535 A vector \(\vec{Q}\) which has a magnitude of 8 is added to the vector \(\vec{P}\), which lies along the \(X\) axis. The resultant of these two vectors is a third vector \(\vec{R}\), which lies along the \(Y\)-axis and has a magnitude twice that of \(\vec{P}\). The magnitude of \(\overrightarrow{\mathbf{P}}\) is:

1 \(\frac{6}{\sqrt{5}}\)
2 \(\frac{8}{\sqrt{5}}\)
3 \(\frac{12}{\sqrt{5}}\)
4 \(\frac{16}{\sqrt{5}}\)
Motion in Plane

143536 Angle (in rad) made by the vector \(\sqrt{3} \hat{\mathbf{i}}+\hat{\mathbf{j}}\) with the \(\mathrm{X}\)-axis:

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
Motion in Plane

143537 The unit vector parallel to resultant of the
vectors \(\vec{A}=4 \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\vec{B}=-\hat{i}+3 \hat{j}-8 \hat{k}\) is:

1 \(\frac{1}{7}(3 \hat{i}+3 \hat{j}-2 \hat{k})\)
2 \(\frac{1}{7}(3 \hat{i}+6 \hat{j}-2 \hat{k})\)
3 \(\frac{1}{49}(3 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-2 \hat{\mathrm{k}})\)
4 \(\frac{1}{49}(3 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
Motion in Plane

143542 The resultant of two forces \(3 P\) and \(2 P\) is \(R\). If the first force is doubled then the resultant is also doubled. The angle between the two forces is :

1 \(90^{\circ}\)
2 \(180^{\circ}\)
3 \(60^{\circ}\)
4 \(120^{\circ}\)
Motion in Plane

143535 A vector \(\vec{Q}\) which has a magnitude of 8 is added to the vector \(\vec{P}\), which lies along the \(X\) axis. The resultant of these two vectors is a third vector \(\vec{R}\), which lies along the \(Y\)-axis and has a magnitude twice that of \(\vec{P}\). The magnitude of \(\overrightarrow{\mathbf{P}}\) is:

1 \(\frac{6}{\sqrt{5}}\)
2 \(\frac{8}{\sqrt{5}}\)
3 \(\frac{12}{\sqrt{5}}\)
4 \(\frac{16}{\sqrt{5}}\)
Motion in Plane

143536 Angle (in rad) made by the vector \(\sqrt{3} \hat{\mathbf{i}}+\hat{\mathbf{j}}\) with the \(\mathrm{X}\)-axis:

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
Motion in Plane

143537 The unit vector parallel to resultant of the
vectors \(\vec{A}=4 \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\vec{B}=-\hat{i}+3 \hat{j}-8 \hat{k}\) is:

1 \(\frac{1}{7}(3 \hat{i}+3 \hat{j}-2 \hat{k})\)
2 \(\frac{1}{7}(3 \hat{i}+6 \hat{j}-2 \hat{k})\)
3 \(\frac{1}{49}(3 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-2 \hat{\mathrm{k}})\)
4 \(\frac{1}{49}(3 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
Motion in Plane

143542 The resultant of two forces \(3 P\) and \(2 P\) is \(R\). If the first force is doubled then the resultant is also doubled. The angle between the two forces is :

1 \(90^{\circ}\)
2 \(180^{\circ}\)
3 \(60^{\circ}\)
4 \(120^{\circ}\)
Motion in Plane

143535 A vector \(\vec{Q}\) which has a magnitude of 8 is added to the vector \(\vec{P}\), which lies along the \(X\) axis. The resultant of these two vectors is a third vector \(\vec{R}\), which lies along the \(Y\)-axis and has a magnitude twice that of \(\vec{P}\). The magnitude of \(\overrightarrow{\mathbf{P}}\) is:

1 \(\frac{6}{\sqrt{5}}\)
2 \(\frac{8}{\sqrt{5}}\)
3 \(\frac{12}{\sqrt{5}}\)
4 \(\frac{16}{\sqrt{5}}\)
Motion in Plane

143536 Angle (in rad) made by the vector \(\sqrt{3} \hat{\mathbf{i}}+\hat{\mathbf{j}}\) with the \(\mathrm{X}\)-axis:

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
Motion in Plane

143537 The unit vector parallel to resultant of the
vectors \(\vec{A}=4 \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\vec{B}=-\hat{i}+3 \hat{j}-8 \hat{k}\) is:

1 \(\frac{1}{7}(3 \hat{i}+3 \hat{j}-2 \hat{k})\)
2 \(\frac{1}{7}(3 \hat{i}+6 \hat{j}-2 \hat{k})\)
3 \(\frac{1}{49}(3 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-2 \hat{\mathrm{k}})\)
4 \(\frac{1}{49}(3 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
Motion in Plane

143542 The resultant of two forces \(3 P\) and \(2 P\) is \(R\). If the first force is doubled then the resultant is also doubled. The angle between the two forces is :

1 \(90^{\circ}\)
2 \(180^{\circ}\)
3 \(60^{\circ}\)
4 \(120^{\circ}\)
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Motion in Plane

143535 A vector \(\vec{Q}\) which has a magnitude of 8 is added to the vector \(\vec{P}\), which lies along the \(X\) axis. The resultant of these two vectors is a third vector \(\vec{R}\), which lies along the \(Y\)-axis and has a magnitude twice that of \(\vec{P}\). The magnitude of \(\overrightarrow{\mathbf{P}}\) is:

1 \(\frac{6}{\sqrt{5}}\)
2 \(\frac{8}{\sqrt{5}}\)
3 \(\frac{12}{\sqrt{5}}\)
4 \(\frac{16}{\sqrt{5}}\)
Motion in Plane

143536 Angle (in rad) made by the vector \(\sqrt{3} \hat{\mathbf{i}}+\hat{\mathbf{j}}\) with the \(\mathrm{X}\)-axis:

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
Motion in Plane

143537 The unit vector parallel to resultant of the
vectors \(\vec{A}=4 \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\vec{B}=-\hat{i}+3 \hat{j}-8 \hat{k}\) is:

1 \(\frac{1}{7}(3 \hat{i}+3 \hat{j}-2 \hat{k})\)
2 \(\frac{1}{7}(3 \hat{i}+6 \hat{j}-2 \hat{k})\)
3 \(\frac{1}{49}(3 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}-2 \hat{\mathrm{k}})\)
4 \(\frac{1}{49}(3 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
Motion in Plane

143542 The resultant of two forces \(3 P\) and \(2 P\) is \(R\). If the first force is doubled then the resultant is also doubled. The angle between the two forces is :

1 \(90^{\circ}\)
2 \(180^{\circ}\)
3 \(60^{\circ}\)
4 \(120^{\circ}\)