DOT PRODUCT AND CROSS PRODUCT
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VECTORS

268945 If \(\vec{A}, \vec{B}\) and \(\vec{C}\) are coplanar vectors, then

1 \((\vec{A} \cdot \vec{B}) \times \vec{C}=0\)
2 \((\vec{A} \times \vec{B}) \cdot \vec{C}=0\)
3 \((\vec{A} \cdot \vec{B}) \cdot \vec{C}=0\)
4 all the above are true
VECTORS

268948 The position vector \(\overrightarrow{\mathrm{r}}\) and linear momentum \(\overrightarrow{\mathrm{P}}\) are \(\overrightarrow{\mathrm{r}}=\hat{\mathrm{i}}\) and \(\overrightarrow{\mathrm{p}}=4 \hat{\mathrm{j}}\) the angular momentum vector is perpendicular to

1 \(x\)-axis
2 \(y\)-axis
3 \(z\)-axis
4 \(x y\)-plane
VECTORS

268949 The vector area of triangle whose sides are \(\vec{a}, \vec{b}, \vec{c}\) is

1 \(\frac{1}{6}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
2 \(\frac{1}{2}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
3 \(\frac{1}{3}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
4 \(\frac{1}{2}|-\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
VECTORS

268950 Set the following vectors in the increasing order of their magnitude.
a) \(3 \hat{i}+4 \hat{j}\)
b) \(2 \hat{i}+4 \hat{j}+6 \hat{k}\)
c) \(2 \hat{i}+2 \hat{j}+2 \hat{k}\)

1 a, b, c
2 c, a, b
3 \(a, c, b\)
4 b, c, a
VECTORS

268951 Arrange the vectors additions so that their magnitudes are in the increasing order.
a) Two vector \(\vec{A}\) and \(\vec{B}\) are parallel
b) Two vectors \(\vec{A}\) and \(\vec{B}\) are antiparallel
c) Two vectors \(\vec{A}\) and \(\vec{B}\) making an angle \(60^{\circ}\)
d) Two vectors \(\vec{A}\) and \(\vec{B}\) making \(120^{\circ}\).

1 b, d, c, a
2 b, c, d, a
3 a, c, d, b
4 c, d, a, b
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VECTORS

268945 If \(\vec{A}, \vec{B}\) and \(\vec{C}\) are coplanar vectors, then

1 \((\vec{A} \cdot \vec{B}) \times \vec{C}=0\)
2 \((\vec{A} \times \vec{B}) \cdot \vec{C}=0\)
3 \((\vec{A} \cdot \vec{B}) \cdot \vec{C}=0\)
4 all the above are true
VECTORS

268948 The position vector \(\overrightarrow{\mathrm{r}}\) and linear momentum \(\overrightarrow{\mathrm{P}}\) are \(\overrightarrow{\mathrm{r}}=\hat{\mathrm{i}}\) and \(\overrightarrow{\mathrm{p}}=4 \hat{\mathrm{j}}\) the angular momentum vector is perpendicular to

1 \(x\)-axis
2 \(y\)-axis
3 \(z\)-axis
4 \(x y\)-plane
VECTORS

268949 The vector area of triangle whose sides are \(\vec{a}, \vec{b}, \vec{c}\) is

1 \(\frac{1}{6}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
2 \(\frac{1}{2}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
3 \(\frac{1}{3}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
4 \(\frac{1}{2}|-\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
VECTORS

268950 Set the following vectors in the increasing order of their magnitude.
a) \(3 \hat{i}+4 \hat{j}\)
b) \(2 \hat{i}+4 \hat{j}+6 \hat{k}\)
c) \(2 \hat{i}+2 \hat{j}+2 \hat{k}\)

1 a, b, c
2 c, a, b
3 \(a, c, b\)
4 b, c, a
VECTORS

268951 Arrange the vectors additions so that their magnitudes are in the increasing order.
a) Two vector \(\vec{A}\) and \(\vec{B}\) are parallel
b) Two vectors \(\vec{A}\) and \(\vec{B}\) are antiparallel
c) Two vectors \(\vec{A}\) and \(\vec{B}\) making an angle \(60^{\circ}\)
d) Two vectors \(\vec{A}\) and \(\vec{B}\) making \(120^{\circ}\).

1 b, d, c, a
2 b, c, d, a
3 a, c, d, b
4 c, d, a, b
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VECTORS

268945 If \(\vec{A}, \vec{B}\) and \(\vec{C}\) are coplanar vectors, then

1 \((\vec{A} \cdot \vec{B}) \times \vec{C}=0\)
2 \((\vec{A} \times \vec{B}) \cdot \vec{C}=0\)
3 \((\vec{A} \cdot \vec{B}) \cdot \vec{C}=0\)
4 all the above are true
VECTORS

268948 The position vector \(\overrightarrow{\mathrm{r}}\) and linear momentum \(\overrightarrow{\mathrm{P}}\) are \(\overrightarrow{\mathrm{r}}=\hat{\mathrm{i}}\) and \(\overrightarrow{\mathrm{p}}=4 \hat{\mathrm{j}}\) the angular momentum vector is perpendicular to

1 \(x\)-axis
2 \(y\)-axis
3 \(z\)-axis
4 \(x y\)-plane
VECTORS

268949 The vector area of triangle whose sides are \(\vec{a}, \vec{b}, \vec{c}\) is

1 \(\frac{1}{6}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
2 \(\frac{1}{2}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
3 \(\frac{1}{3}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
4 \(\frac{1}{2}|-\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
VECTORS

268950 Set the following vectors in the increasing order of their magnitude.
a) \(3 \hat{i}+4 \hat{j}\)
b) \(2 \hat{i}+4 \hat{j}+6 \hat{k}\)
c) \(2 \hat{i}+2 \hat{j}+2 \hat{k}\)

1 a, b, c
2 c, a, b
3 \(a, c, b\)
4 b, c, a
VECTORS

268951 Arrange the vectors additions so that their magnitudes are in the increasing order.
a) Two vector \(\vec{A}\) and \(\vec{B}\) are parallel
b) Two vectors \(\vec{A}\) and \(\vec{B}\) are antiparallel
c) Two vectors \(\vec{A}\) and \(\vec{B}\) making an angle \(60^{\circ}\)
d) Two vectors \(\vec{A}\) and \(\vec{B}\) making \(120^{\circ}\).

1 b, d, c, a
2 b, c, d, a
3 a, c, d, b
4 c, d, a, b
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VECTORS

268945 If \(\vec{A}, \vec{B}\) and \(\vec{C}\) are coplanar vectors, then

1 \((\vec{A} \cdot \vec{B}) \times \vec{C}=0\)
2 \((\vec{A} \times \vec{B}) \cdot \vec{C}=0\)
3 \((\vec{A} \cdot \vec{B}) \cdot \vec{C}=0\)
4 all the above are true
VECTORS

268948 The position vector \(\overrightarrow{\mathrm{r}}\) and linear momentum \(\overrightarrow{\mathrm{P}}\) are \(\overrightarrow{\mathrm{r}}=\hat{\mathrm{i}}\) and \(\overrightarrow{\mathrm{p}}=4 \hat{\mathrm{j}}\) the angular momentum vector is perpendicular to

1 \(x\)-axis
2 \(y\)-axis
3 \(z\)-axis
4 \(x y\)-plane
VECTORS

268949 The vector area of triangle whose sides are \(\vec{a}, \vec{b}, \vec{c}\) is

1 \(\frac{1}{6}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
2 \(\frac{1}{2}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
3 \(\frac{1}{3}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
4 \(\frac{1}{2}|-\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
VECTORS

268950 Set the following vectors in the increasing order of their magnitude.
a) \(3 \hat{i}+4 \hat{j}\)
b) \(2 \hat{i}+4 \hat{j}+6 \hat{k}\)
c) \(2 \hat{i}+2 \hat{j}+2 \hat{k}\)

1 a, b, c
2 c, a, b
3 \(a, c, b\)
4 b, c, a
VECTORS

268951 Arrange the vectors additions so that their magnitudes are in the increasing order.
a) Two vector \(\vec{A}\) and \(\vec{B}\) are parallel
b) Two vectors \(\vec{A}\) and \(\vec{B}\) are antiparallel
c) Two vectors \(\vec{A}\) and \(\vec{B}\) making an angle \(60^{\circ}\)
d) Two vectors \(\vec{A}\) and \(\vec{B}\) making \(120^{\circ}\).

1 b, d, c, a
2 b, c, d, a
3 a, c, d, b
4 c, d, a, b
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VECTORS

268945 If \(\vec{A}, \vec{B}\) and \(\vec{C}\) are coplanar vectors, then

1 \((\vec{A} \cdot \vec{B}) \times \vec{C}=0\)
2 \((\vec{A} \times \vec{B}) \cdot \vec{C}=0\)
3 \((\vec{A} \cdot \vec{B}) \cdot \vec{C}=0\)
4 all the above are true
VECTORS

268948 The position vector \(\overrightarrow{\mathrm{r}}\) and linear momentum \(\overrightarrow{\mathrm{P}}\) are \(\overrightarrow{\mathrm{r}}=\hat{\mathrm{i}}\) and \(\overrightarrow{\mathrm{p}}=4 \hat{\mathrm{j}}\) the angular momentum vector is perpendicular to

1 \(x\)-axis
2 \(y\)-axis
3 \(z\)-axis
4 \(x y\)-plane
VECTORS

268949 The vector area of triangle whose sides are \(\vec{a}, \vec{b}, \vec{c}\) is

1 \(\frac{1}{6}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
2 \(\frac{1}{2}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
3 \(\frac{1}{3}|\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
4 \(\frac{1}{2}|-\vec{b} \times \vec{c}+\vec{c} \times \vec{a}+\vec{a} \times \vec{b}|\)
VECTORS

268950 Set the following vectors in the increasing order of their magnitude.
a) \(3 \hat{i}+4 \hat{j}\)
b) \(2 \hat{i}+4 \hat{j}+6 \hat{k}\)
c) \(2 \hat{i}+2 \hat{j}+2 \hat{k}\)

1 a, b, c
2 c, a, b
3 \(a, c, b\)
4 b, c, a
VECTORS

268951 Arrange the vectors additions so that their magnitudes are in the increasing order.
a) Two vector \(\vec{A}\) and \(\vec{B}\) are parallel
b) Two vectors \(\vec{A}\) and \(\vec{B}\) are antiparallel
c) Two vectors \(\vec{A}\) and \(\vec{B}\) making an angle \(60^{\circ}\)
d) Two vectors \(\vec{A}\) and \(\vec{B}\) making \(120^{\circ}\).

1 b, d, c, a
2 b, c, d, a
3 a, c, d, b
4 c, d, a, b