what is angle resultant of vectors 2i cap + 5j cap and i cap - 2 j cap with the y-axis
Option - 30°,45° , 60° and 90°
pls send correct answer fast I will mark you brainiest answer plsssssss
Answers
Answer:
No, it is not possible to obtain zero by adding two vectors of unequal magnitudes.
Example: Let us add two vectors
→
A
and
→
B
of unequal magnitudes acting in opposite directions. The resultant vector is given by
R=
√
A2+B2+2ABcosθ
If two vectors are exactly opposite to each other, then
θ=180°, cos180°=-1R=
√
A2+B2-2AB
⇒R=
√
(A-B)2
⇒R=(A-B) or (B-A)
From the above equation, we can say that the resultant vector is zero (R = 0) when the magnitudes of the vectors
→
A
and
→
B
are equal (A = B) and both are acting in the opposite directions.
Yes, it is possible to add three vectors of equal magnitudes and get zero.
Lets take three vectors of equal magnitudes
→
A,
→
B
and
→
C
, given these three vectors make an angle of 120° with each other. Consider the figure below:
Lets examine the components of the three vectors.
Ax=AAy=0Bx=-B cos 60°By=B sin 60°Cx=-C cos 60°Cy=-C sin 60°Here, A=B=CSo, along the x-axis , we have:A-(2A cos 60°)=0, as cos 60°=
1
2
⇒B sin 60°-C sin 60°=0
Hence, proved.
Answer:
Answer:
No, it is not possible to obtain zero by adding two vectors of unequal magnitudes.
Example: Let us add two vectors
→
A
and
→
B
of unequal magnitudes acting in opposite directions. The resultant vector is given by
R=
√
A2+B2+2ABcosθ
If two vectors are exactly opposite to each other, then
θ=180°, cos180°=-1R=
√
A2+B2-2AB
⇒R=
√
(A-B)2
⇒R=(A-B) or (B-A)
From the above equation, we can say that the resultant vector is zero (R = 0) when the magnitudes of the vectors
→
A
and
→
B
are equal (A = B) and both are acting in the opposite directions.
Yes, it is possible to add three vectors of equal magnitudes and get zero.
Lets take three vectors of equal magnitudes
→
A,
→
B
and
→
C
, given these three vectors make an angle of 120° with each other. Consider the figure below:
Lets examine the components of the three vectors.
Ax=AAy=0Bx=-B cos 60°By=B sin 60°Cx=-C cos 60°Cy=-C sin 60°Here, A=B=CSo, along the x-axis , we have:A-(2A cos 60°)=0, as cos 60°=
1
2
⇒B sin 60°-C sin 60°=0
Hence, proved.