VECTOR PRODUCT (OR) CROSS PRODUCT
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Rotational Motion

269283 If\(\vec{P} \times \vec{Q}=\vec{R} ; \vec{Q} \times \vec{R}=\vec{P}\) and \(\vec{R} \times \vec{P}=\vec{Q}\) then

1 \(\vec{P}, \vec{Q}\) and \(\vec{R}\) are coplanar
2 angle between\(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) may be less than \(90^{\circ}\)
3 \(\vec{P}+\vec{Q}+\vec{R}\) cannot be equal to zero.
4 \(\vec{P}, \vec{Q}\) and \(\vec{R}\) are mutually perpendicular
Rotational Motion

269372 The angular velocity of a rotating body is\(\vec{\omega}=4 \hat{i}+\hat{j}-2 \hat{k}\). The linear velocity of the body whose position vector \(2 \hat{i}+3 \hat{j}-3 \hat{k}\) is

1 \(5 \hat{i}+8 \hat{j}+14 \hat{k}\)
2 \(3 \hat{i}+8 \hat{j}+10 \hat{k}\)
3 \(8 \hat{i}-3 \hat{j}+2 \hat{k}\)
4 \(-8 \hat{i}+3 \hat{j}+2 \hat{k}\)
Rotational Motion

269373 The area of the triangle whose adjacent sides are represented by the vector\((4 \hat{i}+3 \hat{j}+4 \hat{k})\) and \(5 \hat{i}\) in sq. units is

1 25
2 12.5
3 50
4 45
Rotational Motion

269374 The angle between the vectors \((\hat{i}+\hat{j}+\hat{k})\) and \((\hat{i}-\hat{j}-\hat{k})\) is

1 \(\sin ^{-1} \frac{\sqrt{8}}{3}\)
2 \(\left.\sin ^{-1} \sqcap \frac{1}{-3}\right\rceil+\frac{\pi}{3}\)
3 \(\cos ^{-1} \frac{\sqrt{8}}{3}\)
4 \(\cos ^{-1} \sqrt{\frac{8}{3}}\)
Rotational Motion

269433 The position of a particle is given by \(\vec{r}=\hat{i}+2 \hat{j}-\hat{k}\) and its momentum is \(\vec{p}=3 \hat{i}+4 \hat{j}-2 \hat{k}\). The angular momentum is perpendicular to

1 \(x\)-axis
2 \(y\)-axis
3 \(z\)-axis
4 line at equal angles to all the axes
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Rotational Motion

269283 If\(\vec{P} \times \vec{Q}=\vec{R} ; \vec{Q} \times \vec{R}=\vec{P}\) and \(\vec{R} \times \vec{P}=\vec{Q}\) then

1 \(\vec{P}, \vec{Q}\) and \(\vec{R}\) are coplanar
2 angle between\(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) may be less than \(90^{\circ}\)
3 \(\vec{P}+\vec{Q}+\vec{R}\) cannot be equal to zero.
4 \(\vec{P}, \vec{Q}\) and \(\vec{R}\) are mutually perpendicular
Rotational Motion

269372 The angular velocity of a rotating body is\(\vec{\omega}=4 \hat{i}+\hat{j}-2 \hat{k}\). The linear velocity of the body whose position vector \(2 \hat{i}+3 \hat{j}-3 \hat{k}\) is

1 \(5 \hat{i}+8 \hat{j}+14 \hat{k}\)
2 \(3 \hat{i}+8 \hat{j}+10 \hat{k}\)
3 \(8 \hat{i}-3 \hat{j}+2 \hat{k}\)
4 \(-8 \hat{i}+3 \hat{j}+2 \hat{k}\)
Rotational Motion

269373 The area of the triangle whose adjacent sides are represented by the vector\((4 \hat{i}+3 \hat{j}+4 \hat{k})\) and \(5 \hat{i}\) in sq. units is

1 25
2 12.5
3 50
4 45
Rotational Motion

269374 The angle between the vectors \((\hat{i}+\hat{j}+\hat{k})\) and \((\hat{i}-\hat{j}-\hat{k})\) is

1 \(\sin ^{-1} \frac{\sqrt{8}}{3}\)
2 \(\left.\sin ^{-1} \sqcap \frac{1}{-3}\right\rceil+\frac{\pi}{3}\)
3 \(\cos ^{-1} \frac{\sqrt{8}}{3}\)
4 \(\cos ^{-1} \sqrt{\frac{8}{3}}\)
Rotational Motion

269433 The position of a particle is given by \(\vec{r}=\hat{i}+2 \hat{j}-\hat{k}\) and its momentum is \(\vec{p}=3 \hat{i}+4 \hat{j}-2 \hat{k}\). The angular momentum is perpendicular to

1 \(x\)-axis
2 \(y\)-axis
3 \(z\)-axis
4 line at equal angles to all the axes
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Rotational Motion

269283 If\(\vec{P} \times \vec{Q}=\vec{R} ; \vec{Q} \times \vec{R}=\vec{P}\) and \(\vec{R} \times \vec{P}=\vec{Q}\) then

1 \(\vec{P}, \vec{Q}\) and \(\vec{R}\) are coplanar
2 angle between\(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) may be less than \(90^{\circ}\)
3 \(\vec{P}+\vec{Q}+\vec{R}\) cannot be equal to zero.
4 \(\vec{P}, \vec{Q}\) and \(\vec{R}\) are mutually perpendicular
Rotational Motion

269372 The angular velocity of a rotating body is\(\vec{\omega}=4 \hat{i}+\hat{j}-2 \hat{k}\). The linear velocity of the body whose position vector \(2 \hat{i}+3 \hat{j}-3 \hat{k}\) is

1 \(5 \hat{i}+8 \hat{j}+14 \hat{k}\)
2 \(3 \hat{i}+8 \hat{j}+10 \hat{k}\)
3 \(8 \hat{i}-3 \hat{j}+2 \hat{k}\)
4 \(-8 \hat{i}+3 \hat{j}+2 \hat{k}\)
Rotational Motion

269373 The area of the triangle whose adjacent sides are represented by the vector\((4 \hat{i}+3 \hat{j}+4 \hat{k})\) and \(5 \hat{i}\) in sq. units is

1 25
2 12.5
3 50
4 45
Rotational Motion

269374 The angle between the vectors \((\hat{i}+\hat{j}+\hat{k})\) and \((\hat{i}-\hat{j}-\hat{k})\) is

1 \(\sin ^{-1} \frac{\sqrt{8}}{3}\)
2 \(\left.\sin ^{-1} \sqcap \frac{1}{-3}\right\rceil+\frac{\pi}{3}\)
3 \(\cos ^{-1} \frac{\sqrt{8}}{3}\)
4 \(\cos ^{-1} \sqrt{\frac{8}{3}}\)
Rotational Motion

269433 The position of a particle is given by \(\vec{r}=\hat{i}+2 \hat{j}-\hat{k}\) and its momentum is \(\vec{p}=3 \hat{i}+4 \hat{j}-2 \hat{k}\). The angular momentum is perpendicular to

1 \(x\)-axis
2 \(y\)-axis
3 \(z\)-axis
4 line at equal angles to all the axes
For More Updates join with Us
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Rotational Motion

269283 If\(\vec{P} \times \vec{Q}=\vec{R} ; \vec{Q} \times \vec{R}=\vec{P}\) and \(\vec{R} \times \vec{P}=\vec{Q}\) then

1 \(\vec{P}, \vec{Q}\) and \(\vec{R}\) are coplanar
2 angle between\(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) may be less than \(90^{\circ}\)
3 \(\vec{P}+\vec{Q}+\vec{R}\) cannot be equal to zero.
4 \(\vec{P}, \vec{Q}\) and \(\vec{R}\) are mutually perpendicular
Rotational Motion

269372 The angular velocity of a rotating body is\(\vec{\omega}=4 \hat{i}+\hat{j}-2 \hat{k}\). The linear velocity of the body whose position vector \(2 \hat{i}+3 \hat{j}-3 \hat{k}\) is

1 \(5 \hat{i}+8 \hat{j}+14 \hat{k}\)
2 \(3 \hat{i}+8 \hat{j}+10 \hat{k}\)
3 \(8 \hat{i}-3 \hat{j}+2 \hat{k}\)
4 \(-8 \hat{i}+3 \hat{j}+2 \hat{k}\)
Rotational Motion

269373 The area of the triangle whose adjacent sides are represented by the vector\((4 \hat{i}+3 \hat{j}+4 \hat{k})\) and \(5 \hat{i}\) in sq. units is

1 25
2 12.5
3 50
4 45
Rotational Motion

269374 The angle between the vectors \((\hat{i}+\hat{j}+\hat{k})\) and \((\hat{i}-\hat{j}-\hat{k})\) is

1 \(\sin ^{-1} \frac{\sqrt{8}}{3}\)
2 \(\left.\sin ^{-1} \sqcap \frac{1}{-3}\right\rceil+\frac{\pi}{3}\)
3 \(\cos ^{-1} \frac{\sqrt{8}}{3}\)
4 \(\cos ^{-1} \sqrt{\frac{8}{3}}\)
Rotational Motion

269433 The position of a particle is given by \(\vec{r}=\hat{i}+2 \hat{j}-\hat{k}\) and its momentum is \(\vec{p}=3 \hat{i}+4 \hat{j}-2 \hat{k}\). The angular momentum is perpendicular to

1 \(x\)-axis
2 \(y\)-axis
3 \(z\)-axis
4 line at equal angles to all the axes
NEET DIGITAL LIBRARY
Rotational Motion

269283 If\(\vec{P} \times \vec{Q}=\vec{R} ; \vec{Q} \times \vec{R}=\vec{P}\) and \(\vec{R} \times \vec{P}=\vec{Q}\) then

1 \(\vec{P}, \vec{Q}\) and \(\vec{R}\) are coplanar
2 angle between\(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) may be less than \(90^{\circ}\)
3 \(\vec{P}+\vec{Q}+\vec{R}\) cannot be equal to zero.
4 \(\vec{P}, \vec{Q}\) and \(\vec{R}\) are mutually perpendicular
Rotational Motion

269372 The angular velocity of a rotating body is\(\vec{\omega}=4 \hat{i}+\hat{j}-2 \hat{k}\). The linear velocity of the body whose position vector \(2 \hat{i}+3 \hat{j}-3 \hat{k}\) is

1 \(5 \hat{i}+8 \hat{j}+14 \hat{k}\)
2 \(3 \hat{i}+8 \hat{j}+10 \hat{k}\)
3 \(8 \hat{i}-3 \hat{j}+2 \hat{k}\)
4 \(-8 \hat{i}+3 \hat{j}+2 \hat{k}\)
Rotational Motion

269373 The area of the triangle whose adjacent sides are represented by the vector\((4 \hat{i}+3 \hat{j}+4 \hat{k})\) and \(5 \hat{i}\) in sq. units is

1 25
2 12.5
3 50
4 45
Rotational Motion

269374 The angle between the vectors \((\hat{i}+\hat{j}+\hat{k})\) and \((\hat{i}-\hat{j}-\hat{k})\) is

1 \(\sin ^{-1} \frac{\sqrt{8}}{3}\)
2 \(\left.\sin ^{-1} \sqcap \frac{1}{-3}\right\rceil+\frac{\pi}{3}\)
3 \(\cos ^{-1} \frac{\sqrt{8}}{3}\)
4 \(\cos ^{-1} \sqrt{\frac{8}{3}}\)
Rotational Motion

269433 The position of a particle is given by \(\vec{r}=\hat{i}+2 \hat{j}-\hat{k}\) and its momentum is \(\vec{p}=3 \hat{i}+4 \hat{j}-2 \hat{k}\). The angular momentum is perpendicular to

1 \(x\)-axis
2 \(y\)-axis
3 \(z\)-axis
4 line at equal angles to all the axes