DOT PRODUCT AND CROSS PRODUCT
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VECTORS

268937 Three vectors satisfy the relation \(\vec{A} \cdot \vec{B}=0\) and \(\vec{A} \cdot \vec{C}=0\), then \(\vec{A}\) is parallel to

1 \(\vec{C}\)
2 \(\vec{B}\)
3 \(\vec{B} \times \vec{C}\)
4 \(\vec{B} \cdot \vec{C}\)
VECTORS

268938 Let \(\vec{F}\) be the force acting on a particle having position vector \(\vec{r}\) and \(\vec{\tau}\) be the torque of this foce about the origin. Then (AIEEE-2003)

1 \(\vec{r} \cdot \vec{F}=0\) and \(\vec{r} \cdot \vec{\tau} \neq 0\)
2 \(\vec{r} \cdot \vec{\tau} \neq 0\) and \(\vec{F} \cdot \vec{\tau}=0\)
3 \(\vec{r} \cdot \vec{\tau} \neq 0\) and \(\vec{F} \cdot \vec{\tau} \neq 0\)
4 \(\vec{r} \cdot \vec{\tau}=0\) and \(\vec{F} \cdot \vec{\tau}=0\)
VECTORS

268939 \((\vec{A} \times \vec{B})+(\vec{B} \times \vec{A})\) is equal to

1 \(2 \mathrm{AB}\)
2 \(A^{2} B^{2}\)
3 zero
4 null vector
VECTORS

268940 If \(\vec{C}=\vec{A} \times \vec{B}\), then \(\vec{C}\) is

1 parallel to \(\vec{A}\)
2 parallel to \(\vec{B}\)
3 perpendicular to \(\vec{A}\) and parallel to \(\vec{B}\)
4 perpendicular to both \(\vec{A}\) and \(\vec{B}\)
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VECTORS

268937 Three vectors satisfy the relation \(\vec{A} \cdot \vec{B}=0\) and \(\vec{A} \cdot \vec{C}=0\), then \(\vec{A}\) is parallel to

1 \(\vec{C}\)
2 \(\vec{B}\)
3 \(\vec{B} \times \vec{C}\)
4 \(\vec{B} \cdot \vec{C}\)
VECTORS

268938 Let \(\vec{F}\) be the force acting on a particle having position vector \(\vec{r}\) and \(\vec{\tau}\) be the torque of this foce about the origin. Then (AIEEE-2003)

1 \(\vec{r} \cdot \vec{F}=0\) and \(\vec{r} \cdot \vec{\tau} \neq 0\)
2 \(\vec{r} \cdot \vec{\tau} \neq 0\) and \(\vec{F} \cdot \vec{\tau}=0\)
3 \(\vec{r} \cdot \vec{\tau} \neq 0\) and \(\vec{F} \cdot \vec{\tau} \neq 0\)
4 \(\vec{r} \cdot \vec{\tau}=0\) and \(\vec{F} \cdot \vec{\tau}=0\)
VECTORS

268939 \((\vec{A} \times \vec{B})+(\vec{B} \times \vec{A})\) is equal to

1 \(2 \mathrm{AB}\)
2 \(A^{2} B^{2}\)
3 zero
4 null vector
VECTORS

268940 If \(\vec{C}=\vec{A} \times \vec{B}\), then \(\vec{C}\) is

1 parallel to \(\vec{A}\)
2 parallel to \(\vec{B}\)
3 perpendicular to \(\vec{A}\) and parallel to \(\vec{B}\)
4 perpendicular to both \(\vec{A}\) and \(\vec{B}\)
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VECTORS

268937 Three vectors satisfy the relation \(\vec{A} \cdot \vec{B}=0\) and \(\vec{A} \cdot \vec{C}=0\), then \(\vec{A}\) is parallel to

1 \(\vec{C}\)
2 \(\vec{B}\)
3 \(\vec{B} \times \vec{C}\)
4 \(\vec{B} \cdot \vec{C}\)
VECTORS

268938 Let \(\vec{F}\) be the force acting on a particle having position vector \(\vec{r}\) and \(\vec{\tau}\) be the torque of this foce about the origin. Then (AIEEE-2003)

1 \(\vec{r} \cdot \vec{F}=0\) and \(\vec{r} \cdot \vec{\tau} \neq 0\)
2 \(\vec{r} \cdot \vec{\tau} \neq 0\) and \(\vec{F} \cdot \vec{\tau}=0\)
3 \(\vec{r} \cdot \vec{\tau} \neq 0\) and \(\vec{F} \cdot \vec{\tau} \neq 0\)
4 \(\vec{r} \cdot \vec{\tau}=0\) and \(\vec{F} \cdot \vec{\tau}=0\)
VECTORS

268939 \((\vec{A} \times \vec{B})+(\vec{B} \times \vec{A})\) is equal to

1 \(2 \mathrm{AB}\)
2 \(A^{2} B^{2}\)
3 zero
4 null vector
VECTORS

268940 If \(\vec{C}=\vec{A} \times \vec{B}\), then \(\vec{C}\) is

1 parallel to \(\vec{A}\)
2 parallel to \(\vec{B}\)
3 perpendicular to \(\vec{A}\) and parallel to \(\vec{B}\)
4 perpendicular to both \(\vec{A}\) and \(\vec{B}\)
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VECTORS

268937 Three vectors satisfy the relation \(\vec{A} \cdot \vec{B}=0\) and \(\vec{A} \cdot \vec{C}=0\), then \(\vec{A}\) is parallel to

1 \(\vec{C}\)
2 \(\vec{B}\)
3 \(\vec{B} \times \vec{C}\)
4 \(\vec{B} \cdot \vec{C}\)
VECTORS

268938 Let \(\vec{F}\) be the force acting on a particle having position vector \(\vec{r}\) and \(\vec{\tau}\) be the torque of this foce about the origin. Then (AIEEE-2003)

1 \(\vec{r} \cdot \vec{F}=0\) and \(\vec{r} \cdot \vec{\tau} \neq 0\)
2 \(\vec{r} \cdot \vec{\tau} \neq 0\) and \(\vec{F} \cdot \vec{\tau}=0\)
3 \(\vec{r} \cdot \vec{\tau} \neq 0\) and \(\vec{F} \cdot \vec{\tau} \neq 0\)
4 \(\vec{r} \cdot \vec{\tau}=0\) and \(\vec{F} \cdot \vec{\tau}=0\)
VECTORS

268939 \((\vec{A} \times \vec{B})+(\vec{B} \times \vec{A})\) is equal to

1 \(2 \mathrm{AB}\)
2 \(A^{2} B^{2}\)
3 zero
4 null vector
VECTORS

268940 If \(\vec{C}=\vec{A} \times \vec{B}\), then \(\vec{C}\) is

1 parallel to \(\vec{A}\)
2 parallel to \(\vec{B}\)
3 perpendicular to \(\vec{A}\) and parallel to \(\vec{B}\)
4 perpendicular to both \(\vec{A}\) and \(\vec{B}\)
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