00. Scalar and Vector Quantities
Motion in Plane

143598 The vectors are given by \(\overrightarrow{\mathbf{A}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\vec{B}=3 \hat{i}+6 \hat{j}+2 \hat{k}\). Another vector \(C\) has the same magnitude as \(B\) but has the same direction as \(\mathrm{A}\). Then which of the following vectors represents \(C\) ?

1 \(\frac{7}{3}(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
2 \(\frac{3}{7}(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
3 \(\frac{7}{9}(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
4 \(\frac{9}{7}(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
Motion in Plane

143599 The (x,y,z) coordinates of two points \(A\) and \(B\) are given respectively as \((0,3,-1)\) and \((-2,6,4)\). The displacement vector form \(A\) to \(B\) may be given by :

1 \(-2 \hat{i}+6 \hat{j}+4 \hat{k}\)
2 \(-2 \hat{i}+3 \hat{j}+3 \hat{k}\)
3 \(-2 \hat{i}+3 \hat{j}+5 \hat{k}\)
4 \(2 \hat{i}-3 \hat{j}-5 \hat{k}\)
Motion in Plane

143600 The resultant of two forces \(P\) and \(Q\) is of magnitude \(P\). If \(P\) be doubled, the resultant will be inclined to \(Q\) at an angle.

1 \(0^{0}\)
2 \(30^{\circ}\)
3 \(60^{\circ}\)
4 \(90^{\circ}\)
Motion in Plane

143601 If \(\vec{a}+\vec{b}=\vec{c}\) and \(a+b=c\), then the angle included between \(\vec{a}\) and \(\vec{b}\) is

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

143598 The vectors are given by \(\overrightarrow{\mathbf{A}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\vec{B}=3 \hat{i}+6 \hat{j}+2 \hat{k}\). Another vector \(C\) has the same magnitude as \(B\) but has the same direction as \(\mathrm{A}\). Then which of the following vectors represents \(C\) ?

1 \(\frac{7}{3}(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
2 \(\frac{3}{7}(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
3 \(\frac{7}{9}(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
4 \(\frac{9}{7}(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
Motion in Plane

143599 The (x,y,z) coordinates of two points \(A\) and \(B\) are given respectively as \((0,3,-1)\) and \((-2,6,4)\). The displacement vector form \(A\) to \(B\) may be given by :

1 \(-2 \hat{i}+6 \hat{j}+4 \hat{k}\)
2 \(-2 \hat{i}+3 \hat{j}+3 \hat{k}\)
3 \(-2 \hat{i}+3 \hat{j}+5 \hat{k}\)
4 \(2 \hat{i}-3 \hat{j}-5 \hat{k}\)
Motion in Plane

143600 The resultant of two forces \(P\) and \(Q\) is of magnitude \(P\). If \(P\) be doubled, the resultant will be inclined to \(Q\) at an angle.

1 \(0^{0}\)
2 \(30^{\circ}\)
3 \(60^{\circ}\)
4 \(90^{\circ}\)
Motion in Plane

143601 If \(\vec{a}+\vec{b}=\vec{c}\) and \(a+b=c\), then the angle included between \(\vec{a}\) and \(\vec{b}\) is

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

143598 The vectors are given by \(\overrightarrow{\mathbf{A}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\vec{B}=3 \hat{i}+6 \hat{j}+2 \hat{k}\). Another vector \(C\) has the same magnitude as \(B\) but has the same direction as \(\mathrm{A}\). Then which of the following vectors represents \(C\) ?

1 \(\frac{7}{3}(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
2 \(\frac{3}{7}(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
3 \(\frac{7}{9}(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
4 \(\frac{9}{7}(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
Motion in Plane

143599 The (x,y,z) coordinates of two points \(A\) and \(B\) are given respectively as \((0,3,-1)\) and \((-2,6,4)\). The displacement vector form \(A\) to \(B\) may be given by :

1 \(-2 \hat{i}+6 \hat{j}+4 \hat{k}\)
2 \(-2 \hat{i}+3 \hat{j}+3 \hat{k}\)
3 \(-2 \hat{i}+3 \hat{j}+5 \hat{k}\)
4 \(2 \hat{i}-3 \hat{j}-5 \hat{k}\)
Motion in Plane

143600 The resultant of two forces \(P\) and \(Q\) is of magnitude \(P\). If \(P\) be doubled, the resultant will be inclined to \(Q\) at an angle.

1 \(0^{0}\)
2 \(30^{\circ}\)
3 \(60^{\circ}\)
4 \(90^{\circ}\)
Motion in Plane

143601 If \(\vec{a}+\vec{b}=\vec{c}\) and \(a+b=c\), then the angle included between \(\vec{a}\) and \(\vec{b}\) is

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

143598 The vectors are given by \(\overrightarrow{\mathbf{A}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\vec{B}=3 \hat{i}+6 \hat{j}+2 \hat{k}\). Another vector \(C\) has the same magnitude as \(B\) but has the same direction as \(\mathrm{A}\). Then which of the following vectors represents \(C\) ?

1 \(\frac{7}{3}(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
2 \(\frac{3}{7}(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
3 \(\frac{7}{9}(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
4 \(\frac{9}{7}(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})\)
Motion in Plane

143599 The (x,y,z) coordinates of two points \(A\) and \(B\) are given respectively as \((0,3,-1)\) and \((-2,6,4)\). The displacement vector form \(A\) to \(B\) may be given by :

1 \(-2 \hat{i}+6 \hat{j}+4 \hat{k}\)
2 \(-2 \hat{i}+3 \hat{j}+3 \hat{k}\)
3 \(-2 \hat{i}+3 \hat{j}+5 \hat{k}\)
4 \(2 \hat{i}-3 \hat{j}-5 \hat{k}\)
Motion in Plane

143600 The resultant of two forces \(P\) and \(Q\) is of magnitude \(P\). If \(P\) be doubled, the resultant will be inclined to \(Q\) at an angle.

1 \(0^{0}\)
2 \(30^{\circ}\)
3 \(60^{\circ}\)
4 \(90^{\circ}\)
Motion in Plane

143601 If \(\vec{a}+\vec{b}=\vec{c}\) and \(a+b=c\), then the angle included between \(\vec{a}\) and \(\vec{b}\) is

1 \(90^{\circ}\)
2 \(180^{\circ}\)
3 \(120^{\circ}\)
4 zero
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here