NEET Physics MCQ: NCERT Vector Resolution in Plane

🔄Ncert Concepts :Vector Addition, Dot Product, Magnitude of a Vector, Trigonometry

2.

What vector must be added to the sum of two vectors $2\hat i - \hat j + 3\hat k\,and\,3\hat i - 2\hat j - 2\hat k$ so that the resultant is a unit vector along Z-axis.

A

$5\hat i + \hat k$

B

$- 5\hat i + 3\hat j$

C

$3\hat j + 5\hat k$

D

$- 3\hat j + 2\hat k$

Question Tags

📑 Chapter:Structure Of Atom

🔄Ncert Concepts :vector addition, unit vector, resultant vector

3.

A child travelling in a train throws a ball outside with a speed V. According to a child who is standing on the ground, the speed of the ball is

A

Same as V

B

Greater than V

C

Less than V

D

None of these

Question Tags

🔄Ncert Concepts :relative velocity, vector addition

4.

If the vector ${\rm{\vec A}} = 2\hat i + 4\hat j\,\,and\,\,{\rm{\vec B}} = 5\hat i + {\rm{p\hat j}}$ are parallel to each other, the magnitude of ${\rm{\vec B}}$ is

A

$5\sqrt 5$

B

10

C

15

D

$2\sqrt 5$

Question Tags

🔄Ncert Concepts :Parallel vectors, Vector magnitude

5.

If $0.5\hat i + 0.8\hat j + {\rm{c\hat k}}$ is a unit vector, then the value of c is

A

$\sqrt {0.11}$

B

$\sqrt {0.22}$

C

$\sqrt {0.33}$

D

$\sqrt {0.89}$

Question Tags

🔄Ncert Concepts :unit vector, magnitude of a vector

6.

The angular velocity of a rotating body is $\mathop \omega \limits^ o = 4\,\widehat {\rm{i}}{\rm{ + }}\widehat {\rm{j}}{\rm{ - 2}}\widehat {\rm{k}}$ . The linear velocity of the body whose position vector $2\widehat {\rm{i}}{\rm{ + 3}}\widehat {\rm{j}}{\rm{ - 3}}\widehat {\rm{k}}$ is

A

$5\,\widehat {\rm{i}}{\rm{ + 8}}\widehat {\rm{j}}{\rm{ + 14}}\widehat {\rm{k}}$

B

$3\,\widehat {\rm{i}}{\rm{ + 8}}\widehat {\rm{j}}{\rm{ + 10}}\widehat {\rm{k}}$

C

$8\,\widehat {\rm{i}} - {\rm{3}}\widehat {\rm{j}}{\rm{ + 2}}\widehat {\rm{k}}$

D

$- 8\,\widehat {\rm{i}}{\rm{ + 3}}\widehat {\rm{j}}{\rm{ + 2}}\widehat {\rm{k}}$

Question Tags

🔄Ncert Concepts :angular velocity, linear velocity, cross product

7.

$\mathop {{\rm{ }}A}\limits^ -   = \mathop {{\rm{ }}B}\limits^ -   + \mathop {{\rm{ }}C}\limits^ -  $ and the magnitudes of $\mathop {{\rm{ }}A}\limits^ -  ,\mathop {{\rm{ }}B}\limits^ -  ,\mathop {{\rm{ }}C}\limits^ -  $ are 5, 4 and 3 units respectively, the angle between $\mathop {{\rm{ }}A}\limits^ -  \mathop {{\rm{ }}C}\limits^ -  $ is:

A

${{\mathop{\rm Cos}

olimits} ^{ - 1}}\left( {\frac{3}{5}} \right)$

B

${{\mathop{\rm Cos}

olimits} ^{ - 1}}\left( {\frac{4}{5}} \right)$

C

$\frac{\pi }{2}$

D

${\sin ^{ - 1}}\left( {\frac{3}{4}} \right)$

Question Tags

📑 Chapter:Structure Of Atom

🔄Ncert Concepts :vector addition, dot product, magnitude of a vector, cosine of an angle

8.

$\mathop {{\rm{ }}A}\limits^ -   = \mathop {{\rm{ }}B}\limits^ -   + \mathop {{\rm{ }}C}\limits^ -  $ and the magnitudes of $\mathop {{\rm{ }}A}\limits^ -  ,\mathop {{\rm{ }}B}\limits^ -  ,\mathop {{\rm{ }}C}\limits^ -  $ are 5, 4 and 3 units respectively, the angle between $\mathop {{\rm{ }}A}\limits^ -  \mathop {{\rm{ }}C}\limits^ -  $ is:

A

${{\mathop{\rm Cos}

olimits} ^{ - 1}}\left( {\frac{3}{5}} \right)$

B

${{\mathop{\rm Cos}

olimits} ^{ - 1}}\left( {\frac{4}{5}} \right)$

C

$\frac{\pi }{2}$

D

${\sin ^{ - 1}}\left( {\frac{3}{4}} \right)$

Question Tags

🔄Ncert Concepts :vector addition, dot product, magnitude of vectors, cosine of angle

9.

If $0.5\hat i + 0.8\hat j + {\rm{c\hat k}}$ is a unit vector, then the value of c is

A

$\sqrt {0.11}$

B

$\sqrt {0.22}$

C

$\sqrt {0.33}$

D

$\sqrt {0.89}$

Question Tags

📑 Chapter:Structure Of Atom