Vectors -… | NUST Entrance Test Mathematics

Find a unit vector in the direction of the vector $v=3i-4j$

Difficulty: Easy

A:

$i-j$

B:

\frac{3}{5}i- \frac{4}{5}j

C:

\frac{1}{3}i- \frac{1}{4}j

D:

\frac{3}{12}i- \frac{4}{12}j

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If u=ai+2j-k and v=i+aj+3k are perpendicular, then a=

Difficulty: Easy

A:

1

B:

2

C:

3

D:

-3

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If u=2ai+j-k and v=i+aj+4k are perpendicular then a=

Difficulty: Easy

A:

4

B:

1/2

C:

3

D:

4/3

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The angle between the vectors u=[-3,5] and v=[6,-2] is:

Difficulty: Easy

A:

-\frac{\pi}{2}

B:

-\frac{3\pi}{2}

C:

\pi

D:

None

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If the angle between the vectors u and v is $\frac{\pi}{2}$ then the vectors u and v are:

Difficulty: Easy

A:

Orthogonal

B:

Collinear

C:

Parallel

D:

All

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If the angle between two vectors u and v is 0 or $\pi$, then the vectors u and v are:

Difficulty: Easy

A:

Orthogonal

B:

Collinear

C:

Perpendicular

D:

None

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The angle between the vectors u=2i-j+k and v=-i+j is:

Difficulty: Easy

A:

\frac{3\pi}{2}

B:

\frac{2\pi}{3}

C:

\frac{5\pi}{6}

D:

\frac{\pi}{3}

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If u=2i+pj+5k and v=3i+j+pk are perpendicular, then p=

Difficulty: Easy

A:

1

B:

2

C:

-1

D:

-3

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The position vector OP in the YZ plane is:

Difficulty: Easy

A:

OP=yj+zk

B:

OP=xi+yj

C:

OP=xi+zk

D:

OP=zi+yk

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If the sum of two unit vectors is a unit vector then the magnitude of their difference is:

Difficulty: Easy

A:

\sqrt{2}

B:

\sqrt{3}

C:

1

D:

None

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Choose the correct options for the following questions.

Find a unit vector in the direction of the vector $v=3i-4j$

If u=ai+2j-k and v=i+aj+3k are perpendicular, then a=

If u=2ai+j-k and v=i+aj+4k are perpendicular then a=

The angle between the vectors u=[-3,5] and v=[6,-2] is:

If the angle between the vectors u and v is $\frac{\pi}{2}$ then the vectors u and v are:

If the angle between two vectors u and v is 0 or $\pi$, then the vectors u and v are:

The angle between the vectors u=2i-j+k and v=-i+j is:

If u=2i+pj+5k and v=3i+j+pk are perpendicular, then p=

The position vector OP in the YZ plane is:

If the sum of two unit vectors is a unit vector then the magnitude of their difference is:

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