Vector Algebra Online Objective Test | Vector Algebra Online Objective Test

Q1. If a vector

\vec{r}

is expressed in component form as

\vec{r} = x \hat{i} + y \hat{j} + z \hat{k}

then the magnitude of the vector

\vec{r}

A. x2+y2+2z2−−−−−−−−−−−√

B. x2+y2+ z2−−−−−−−−−−−√2

C. x2+2y2+z2−−−−−−−−−−−√

D. x2+y2+z2−−−−−−−−−−−√

Answer : Option D
Explaination / Solution:

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Q2. If a vector

\vec{r}

is expressed in component form as

\vec{r} = x \hat{i} + y \hat{j} + z \hat{k}

then x, y and z are referred to as

A. unit scalars

B. scaling factors

C. vector components or rectangular components

D. unit vectors

Answer : Option C
Explaination / Solution:

In

\vec{r}

\vec{r} = x \hat{i} + y \hat{j} + z \hat{k}

x , y and z represents the components of

\vec{r}

along x-axis ,y-axis and z-axis respectively.

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Q3. Which of the following is a vector?

A. acceleration

B. charge

C. energy

D. mass

Answer : Option A
Explaination / Solution:

Acceleration is a vector quantity , because acceleration is defined as the rate of change of velocity w.r.t. time.and velocity specifies direction

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Q4. In the figure which are the Equal vectors?

Answer : Option B
Explaination / Solution:

are equal vectors , because they have equal magnitude and same direction.

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Q5. In the figure which are the collinear vectors?

Answer : Option B
Explaination / Solution:

are collinear vectors , because are parallel in direction and same magnitude.

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Q6.

are

A. collinear

B. orthogonal vectors

C. not equal and not collinear

D. equal

Answer : Option A
Explaination / Solution:

are collinear vectors , because they are parallel in direction and having the same magnitude.

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Q7. If two vectors have their corresponding direction cosines equal then the two vectors

A. are at an angle of

55^{\circ}

B. are parallel

C. are perpendicular

D. are at an angle of

45^{\circ}

Answer : Option B
Explaination / Solution:

If the direction cosines of two vectors are same , then the vectors are said to be parallel.

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Q8. In triangle ABC, which of the following is not true?

A. .

\vec{A B} + \vec{B C} - \vec{C A} = 0

B. AB−→−+BC−→−+AC−→−=0

C. AB−→−−CB−→−+CA−→−=0

D. .

\vec{A B} + \vec{B C} - \vec{C A} = 0

Answer : Option B
Explaination / Solution:

\vec{A B} + \vec{B C} = \vec{A C}

(triangle law of vector addition) but

\vec{A C} = - \vec{C A}

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Q9. If

are two collinear vectors, then which of the following are incorrect

A. both the vectors

have same direction, but different magnitudes.

B. the respective components of

are not proportional

Answer : Option A
Explaination / Solution:

If

are two collinear vectors, then, they are parallel to the same line irrespective of their magnitudes and directions.

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Q10. Magnitude of the vector

A. √63

B. √61

C. √62

D. √65

Answer : Option C
Explaination / Solution:

Total Question/Mark :
Scored Mark :
Mark for Correct Answer : 1
Mark for Wrong Answer : -0.5
Mark for Left Answer : 0

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