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VECTORS

268998 Find the value of $(\vec{a} + \vec{b}) \times (\vec{a} - \vec{b}) =$

1

(\vec{a} \times \vec{b})

2

2 (\vec{a} \times \vec{b})

3

- 2 (\vec{a} \cdot \vec{b})

4

- 2 (\vec{a} \times \vec{b})

VECTORS

268978 If $\vec{F} = 2 \hat{i} + 3 \hat{j} - \hat{k}$ and $\vec{r} = \hat{i} - \hat{j} + 6 \hat{k}$ find $\vec{r} \times \vec{F}$

1

- 17 \hat{i} + 13 \hat{j} + 5 \hat{k}

2

- 17 \hat{i} - 13 \hat{j} - 5 \hat{k}

3

3 \hat{i} + 4 \hat{j} - 5 \hat{k}

4

- 3 \hat{i} - 4 \hat{j} + 5 \hat{k}

Explanation:

$\vec{r} \times \vec{F} = | \begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 1 & - 1 & 6 \\ 2 & 3 & - 1 \end{array} |$

VECTORS

268979 Two sides of a triangle are given by $\hat{i} + \hat{j} + \hat{k}$ and $\hat{i} + 2 \hat{j} + 3 \hat{k}$ , then area of triangle is

1

\sqrt{26}

2

\sqrt{26} / 2

3

\sqrt{46}

4 26

Explanation:

Area of triangle $= \frac{1}{2} | \vec{A} \times \vec{B} |$

VECTORS

268980 The magnitude of scalar and vector products of two vectors are 144 and $48 \sqrt{3}$ respectively. What is the angle between the two vectors ?

1

30^{\circ}

2

45^{\circ}

3

60^{\circ}

4

90^{0}

Explanation:

$a b \cos θ = 144, a b \sin θ = 48 \sqrt{3}$

VECTORS

268981 Area of a parallelogram formed by vectors $(3 \hat{i} - 2 \hat{j} + \hat{k}) m$ and $(\hat{i} + 2 \hat{j} + 3 \hat{k})$ masadjacentsides is

1

3 \sqrt{8} m^{2}

2

24 m^{2}

3

8 \sqrt{3} m^{2}

4

4 \sqrt{3} m^{2}

Explanation:

Area of parallelogram $= | \vec{A} \times \vec{B} |$

VECTORS

268998 Find the value of $(\vec{a} + \vec{b}) \times (\vec{a} - \vec{b}) =$

1

(\vec{a} \times \vec{b})

2

2 (\vec{a} \times \vec{b})

3

- 2 (\vec{a} \cdot \vec{b})

4

- 2 (\vec{a} \times \vec{b})

VECTORS

268978 If $\vec{F} = 2 \hat{i} + 3 \hat{j} - \hat{k}$ and $\vec{r} = \hat{i} - \hat{j} + 6 \hat{k}$ find $\vec{r} \times \vec{F}$

1

- 17 \hat{i} + 13 \hat{j} + 5 \hat{k}

2

- 17 \hat{i} - 13 \hat{j} - 5 \hat{k}

3

3 \hat{i} + 4 \hat{j} - 5 \hat{k}

4

- 3 \hat{i} - 4 \hat{j} + 5 \hat{k}

Explanation:

$\vec{r} \times \vec{F} = | \begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 1 & - 1 & 6 \\ 2 & 3 & - 1 \end{array} |$

VECTORS

268979 Two sides of a triangle are given by $\hat{i} + \hat{j} + \hat{k}$ and $\hat{i} + 2 \hat{j} + 3 \hat{k}$ , then area of triangle is

1

\sqrt{26}

2

\sqrt{26} / 2

3

\sqrt{46}

4 26

Explanation:

Area of triangle $= \frac{1}{2} | \vec{A} \times \vec{B} |$

VECTORS

268980 The magnitude of scalar and vector products of two vectors are 144 and $48 \sqrt{3}$ respectively. What is the angle between the two vectors ?

1

30^{\circ}

2

45^{\circ}

3

60^{\circ}

4

90^{0}

Explanation:

$a b \cos θ = 144, a b \sin θ = 48 \sqrt{3}$

VECTORS

268981 Area of a parallelogram formed by vectors $(3 \hat{i} - 2 \hat{j} + \hat{k}) m$ and $(\hat{i} + 2 \hat{j} + 3 \hat{k})$ masadjacentsides is

1

3 \sqrt{8} m^{2}

2

24 m^{2}

3

8 \sqrt{3} m^{2}

4

4 \sqrt{3} m^{2}

Explanation:

Area of parallelogram $= | \vec{A} \times \vec{B} |$

VECTORS

268998 Find the value of $(\vec{a} + \vec{b}) \times (\vec{a} - \vec{b}) =$

1

(\vec{a} \times \vec{b})

2

2 (\vec{a} \times \vec{b})

3

- 2 (\vec{a} \cdot \vec{b})

4

- 2 (\vec{a} \times \vec{b})

VECTORS

268978 If $\vec{F} = 2 \hat{i} + 3 \hat{j} - \hat{k}$ and $\vec{r} = \hat{i} - \hat{j} + 6 \hat{k}$ find $\vec{r} \times \vec{F}$

1

- 17 \hat{i} + 13 \hat{j} + 5 \hat{k}

2

- 17 \hat{i} - 13 \hat{j} - 5 \hat{k}

3

3 \hat{i} + 4 \hat{j} - 5 \hat{k}

4

- 3 \hat{i} - 4 \hat{j} + 5 \hat{k}

Explanation:

$\vec{r} \times \vec{F} = | \begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 1 & - 1 & 6 \\ 2 & 3 & - 1 \end{array} |$

VECTORS

268979 Two sides of a triangle are given by $\hat{i} + \hat{j} + \hat{k}$ and $\hat{i} + 2 \hat{j} + 3 \hat{k}$ , then area of triangle is

1

\sqrt{26}

2

\sqrt{26} / 2

3

\sqrt{46}

4 26

Explanation:

Area of triangle $= \frac{1}{2} | \vec{A} \times \vec{B} |$

VECTORS

268980 The magnitude of scalar and vector products of two vectors are 144 and $48 \sqrt{3}$ respectively. What is the angle between the two vectors ?

1

30^{\circ}

2

45^{\circ}

3

60^{\circ}

4

90^{0}

Explanation:

$a b \cos θ = 144, a b \sin θ = 48 \sqrt{3}$

VECTORS

268981 Area of a parallelogram formed by vectors $(3 \hat{i} - 2 \hat{j} + \hat{k}) m$ and $(\hat{i} + 2 \hat{j} + 3 \hat{k})$ masadjacentsides is

1

3 \sqrt{8} m^{2}

2

24 m^{2}

3

8 \sqrt{3} m^{2}

4

4 \sqrt{3} m^{2}

Explanation:

Area of parallelogram $= | \vec{A} \times \vec{B} |$

VECTORS

268998 Find the value of $(\vec{a} + \vec{b}) \times (\vec{a} - \vec{b}) =$

1

(\vec{a} \times \vec{b})

2

2 (\vec{a} \times \vec{b})

3

- 2 (\vec{a} \cdot \vec{b})

4

- 2 (\vec{a} \times \vec{b})

VECTORS

268978 If $\vec{F} = 2 \hat{i} + 3 \hat{j} - \hat{k}$ and $\vec{r} = \hat{i} - \hat{j} + 6 \hat{k}$ find $\vec{r} \times \vec{F}$

1

- 17 \hat{i} + 13 \hat{j} + 5 \hat{k}

2

- 17 \hat{i} - 13 \hat{j} - 5 \hat{k}

3

3 \hat{i} + 4 \hat{j} - 5 \hat{k}

4

- 3 \hat{i} - 4 \hat{j} + 5 \hat{k}

Explanation:

$\vec{r} \times \vec{F} = | \begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 1 & - 1 & 6 \\ 2 & 3 & - 1 \end{array} |$

VECTORS

268979 Two sides of a triangle are given by $\hat{i} + \hat{j} + \hat{k}$ and $\hat{i} + 2 \hat{j} + 3 \hat{k}$ , then area of triangle is

1

\sqrt{26}

2

\sqrt{26} / 2

3

\sqrt{46}

4 26

Explanation:

Area of triangle $= \frac{1}{2} | \vec{A} \times \vec{B} |$

VECTORS

268980 The magnitude of scalar and vector products of two vectors are 144 and $48 \sqrt{3}$ respectively. What is the angle between the two vectors ?

1

30^{\circ}

2

45^{\circ}

3

60^{\circ}

4

90^{0}

Explanation:

$a b \cos θ = 144, a b \sin θ = 48 \sqrt{3}$

VECTORS

268981 Area of a parallelogram formed by vectors $(3 \hat{i} - 2 \hat{j} + \hat{k}) m$ and $(\hat{i} + 2 \hat{j} + 3 \hat{k})$ masadjacentsides is

1

3 \sqrt{8} m^{2}

2

24 m^{2}

3

8 \sqrt{3} m^{2}

4

4 \sqrt{3} m^{2}

Explanation:

Area of parallelogram $= | \vec{A} \times \vec{B} |$

VECTORS

268998 Find the value of $(\vec{a} + \vec{b}) \times (\vec{a} - \vec{b}) =$

1

(\vec{a} \times \vec{b})

2

2 (\vec{a} \times \vec{b})

3

- 2 (\vec{a} \cdot \vec{b})

4

- 2 (\vec{a} \times \vec{b})

VECTORS

268978 If $\vec{F} = 2 \hat{i} + 3 \hat{j} - \hat{k}$ and $\vec{r} = \hat{i} - \hat{j} + 6 \hat{k}$ find $\vec{r} \times \vec{F}$

1

- 17 \hat{i} + 13 \hat{j} + 5 \hat{k}

2

- 17 \hat{i} - 13 \hat{j} - 5 \hat{k}

3

3 \hat{i} + 4 \hat{j} - 5 \hat{k}

4

- 3 \hat{i} - 4 \hat{j} + 5 \hat{k}

Explanation:

$\vec{r} \times \vec{F} = | \begin{array}{ccc} \hat{i} & \hat{j} & \hat{k} \\ 1 & - 1 & 6 \\ 2 & 3 & - 1 \end{array} |$

VECTORS

268979 Two sides of a triangle are given by $\hat{i} + \hat{j} + \hat{k}$ and $\hat{i} + 2 \hat{j} + 3 \hat{k}$ , then area of triangle is

1

\sqrt{26}

2

\sqrt{26} / 2

3

\sqrt{46}

4 26

Explanation:

Area of triangle $= \frac{1}{2} | \vec{A} \times \vec{B} |$

VECTORS

268980 The magnitude of scalar and vector products of two vectors are 144 and $48 \sqrt{3}$ respectively. What is the angle between the two vectors ?

1

30^{\circ}

2

45^{\circ}

3

60^{\circ}

4

90^{0}

Explanation:

$a b \cos θ = 144, a b \sin θ = 48 \sqrt{3}$

VECTORS

268981 Area of a parallelogram formed by vectors $(3 \hat{i} - 2 \hat{j} + \hat{k}) m$ and $(\hat{i} + 2 \hat{j} + 3 \hat{k})$ masadjacentsides is

1

3 \sqrt{8} m^{2}

2

24 m^{2}

3

8 \sqrt{3} m^{2}

4

4 \sqrt{3} m^{2}

Explanation:

Area of parallelogram $= | \vec{A} \times \vec{B} |$