Vector components Quiz 1

Question 1

Given that the components of the vector $$\overrightarrow{A}$$ along the x-axis and y-axis are 4 and 3 respectively. Find the orientation of the vector. $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/901aa4c1-e1e5-4818-a814-0ae177efa8aa6693493699038594517.png"/>

Accepted Answer

36$${}^\circ $$51’

Answer

30$${}^\circ $$25’

Answer

60$${}^\circ $$2’

Answer

45$${}^\circ $$13’

Question 2

Consider a vector whose length is 5 cm and it is oriented $$30{}^\circ $$ with the positive X-axis. Calculate it’s projections along the X and Y axis. $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/194cf1e1-3cf5-4db9-8f34-be279de9b7da7744933083820901972.png"/>

Accepted Answer

x=4.3,  y=2.5

Answer

x=2.5,  y=4.3

Answer

x=3.9, y=4.9

Answer

x=4.9,  y=3.9

Question 3

Calculate the projection of a vector along x-axis, whose length is 5 cm and it’s orientation with y-axis is $$60{}^\circ $$. $$ \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/f17e2408-f2e2-4f80-b817-23eb2f38e5771123141682216910984.png"/>

Accepted Answer

4.3

Answer

5.4

Answer

3.3

Answer

6.4

Question 4

If vector $$\overrightarrow{{{F}_{1}}}=5\hat{i}+6\hat{j}+2\hat{k}$$ represents the force exerted by object 1 on a table and $$\overrightarrow{{{F}_{2}}}=7\hat{j}+3\hat{k}$$ is the force exerted by the 2nd object on the table. Calculate the magnitude of the combined force exerted by both the objects on the table.

Accepted Answer

14.7

Answer

12.5

Answer

10.5

Answer

4.6

Question 5

If the $$x, y$$ and $$z$$ projection of a vector is 3 along x-axis, 4 along y-axis and 0 along z-axis. Calculate the length of the vector from the origin.

Accepted Answer

5

Answer

4

Answer

3

Answer

6