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VECTORS

268964 The direction cosines of a vector $\vec{A}$ are $\cos α = \frac{4}{5 \sqrt{2}}, \cos β = \frac{1}{\sqrt{2}}$ and $\cos γ = \frac{3}{5 \sqrt{2}}$ then the vector $\vec{A}$ is

1

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

2

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

3

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

4

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

Explanation:

$\vec{A} = A_{x} \hat{i} + A_{y} \hat{j} + A_{z} \hat{k}$

VECTORS

268965 Given two vectors $\vec{A} = \hat{i} - 2 \hat{j} - 3 \hat{k}$ and $\vec{B} = 4 \hat{i} - 2 \hat{j} + 6 \hat{k}$ . The angle made by $(\vec{A} + \vec{B})$ with the $X$ - axis is

1

30^{\circ}

2

45^{\circ}

3

60^{\circ}

4

90^{\circ}

(2007 M)

Explanation:

$\cos θ = \frac{x}{\sqrt{x^{2} + y^{2} + z^{2}}}$

VECTORS

268966 To go from town $A$ to town $B$ a plane must fly about $1780 km$ atan angle of $30^{\circ}$ West of north. How far West of $A$ is $B$ ?

1

1542 km

2

1452 km 3)

3

1254 km 4) 8

4

890 km

Explanation:

$x = d \sin θ$

VECTORS

268967 A vector $\hat{i} + \sqrt{3} \hat{j}$ rotates about its tail through an angle $60^{\circ}$ in clockwise direction then the new vector is

1

\hat{i} + \sqrt{3} \hat{j}

2

3 \hat{i} - 4 \hat{j}

3

2 \hat{j}

4

2 \hat{i}

Explanation:

w.r.t x-axis initially $θ = 60^{\circ}, | \vec{A} | = 2$ units on rotation $θ^{1} = 0^{0}, | \vec{A} |^{1} = 2$ units

VECTORS

268964 The direction cosines of a vector $\vec{A}$ are $\cos α = \frac{4}{5 \sqrt{2}}, \cos β = \frac{1}{\sqrt{2}}$ and $\cos γ = \frac{3}{5 \sqrt{2}}$ then the vector $\vec{A}$ is

1

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

2

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

3

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

4

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

Explanation:

$\vec{A} = A_{x} \hat{i} + A_{y} \hat{j} + A_{z} \hat{k}$

VECTORS

268965 Given two vectors $\vec{A} = \hat{i} - 2 \hat{j} - 3 \hat{k}$ and $\vec{B} = 4 \hat{i} - 2 \hat{j} + 6 \hat{k}$ . The angle made by $(\vec{A} + \vec{B})$ with the $X$ - axis is

1

30^{\circ}

2

45^{\circ}

3

60^{\circ}

4

90^{\circ}

(2007 M)

Explanation:

$\cos θ = \frac{x}{\sqrt{x^{2} + y^{2} + z^{2}}}$

VECTORS

268966 To go from town $A$ to town $B$ a plane must fly about $1780 km$ atan angle of $30^{\circ}$ West of north. How far West of $A$ is $B$ ?

1

1542 km

2

1452 km 3)

3

1254 km 4) 8

4

890 km

Explanation:

$x = d \sin θ$

VECTORS

268967 A vector $\hat{i} + \sqrt{3} \hat{j}$ rotates about its tail through an angle $60^{\circ}$ in clockwise direction then the new vector is

1

\hat{i} + \sqrt{3} \hat{j}

2

3 \hat{i} - 4 \hat{j}

3

2 \hat{j}

4

2 \hat{i}

Explanation:

w.r.t x-axis initially $θ = 60^{\circ}, | \vec{A} | = 2$ units on rotation $θ^{1} = 0^{0}, | \vec{A} |^{1} = 2$ units

VECTORS

268964 The direction cosines of a vector $\vec{A}$ are $\cos α = \frac{4}{5 \sqrt{2}}, \cos β = \frac{1}{\sqrt{2}}$ and $\cos γ = \frac{3}{5 \sqrt{2}}$ then the vector $\vec{A}$ is

1

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

2

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

3

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

4

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

Explanation:

$\vec{A} = A_{x} \hat{i} + A_{y} \hat{j} + A_{z} \hat{k}$

VECTORS

268965 Given two vectors $\vec{A} = \hat{i} - 2 \hat{j} - 3 \hat{k}$ and $\vec{B} = 4 \hat{i} - 2 \hat{j} + 6 \hat{k}$ . The angle made by $(\vec{A} + \vec{B})$ with the $X$ - axis is

1

30^{\circ}

2

45^{\circ}

3

60^{\circ}

4

90^{\circ}

(2007 M)

Explanation:

$\cos θ = \frac{x}{\sqrt{x^{2} + y^{2} + z^{2}}}$

VECTORS

268966 To go from town $A$ to town $B$ a plane must fly about $1780 km$ atan angle of $30^{\circ}$ West of north. How far West of $A$ is $B$ ?

1

1542 km

2

1452 km 3)

3

1254 km 4) 8

4

890 km

Explanation:

$x = d \sin θ$

VECTORS

268967 A vector $\hat{i} + \sqrt{3} \hat{j}$ rotates about its tail through an angle $60^{\circ}$ in clockwise direction then the new vector is

1

\hat{i} + \sqrt{3} \hat{j}

2

3 \hat{i} - 4 \hat{j}

3

2 \hat{j}

4

2 \hat{i}

Explanation:

w.r.t x-axis initially $θ = 60^{\circ}, | \vec{A} | = 2$ units on rotation $θ^{1} = 0^{0}, | \vec{A} |^{1} = 2$ units

VECTORS

268964 The direction cosines of a vector $\vec{A}$ are $\cos α = \frac{4}{5 \sqrt{2}}, \cos β = \frac{1}{\sqrt{2}}$ and $\cos γ = \frac{3}{5 \sqrt{2}}$ then the vector $\vec{A}$ is

1

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

2

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

3

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

4

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

Explanation:

$\vec{A} = A_{x} \hat{i} + A_{y} \hat{j} + A_{z} \hat{k}$

VECTORS

268965 Given two vectors $\vec{A} = \hat{i} - 2 \hat{j} - 3 \hat{k}$ and $\vec{B} = 4 \hat{i} - 2 \hat{j} + 6 \hat{k}$ . The angle made by $(\vec{A} + \vec{B})$ with the $X$ - axis is

1

30^{\circ}

2

45^{\circ}

3

60^{\circ}

4

90^{\circ}

(2007 M)

Explanation:

$\cos θ = \frac{x}{\sqrt{x^{2} + y^{2} + z^{2}}}$

VECTORS

268966 To go from town $A$ to town $B$ a plane must fly about $1780 km$ atan angle of $30^{\circ}$ West of north. How far West of $A$ is $B$ ?

1

1542 km

2

1452 km 3)

3

1254 km 4) 8

4

890 km

Explanation:

$x = d \sin θ$

VECTORS

268967 A vector $\hat{i} + \sqrt{3} \hat{j}$ rotates about its tail through an angle $60^{\circ}$ in clockwise direction then the new vector is

1

\hat{i} + \sqrt{3} \hat{j}

2

3 \hat{i} - 4 \hat{j}

3

2 \hat{j}

4

2 \hat{i}

Explanation:

w.r.t x-axis initially $θ = 60^{\circ}, | \vec{A} | = 2$ units on rotation $θ^{1} = 0^{0}, | \vec{A} |^{1} = 2$ units

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