Physics, asked by Anonymous, 1 year ago

there r two vectors A and B such that A+B=A-B then find the angle between A and B

Answers

Answered by Tamanna05
26
I assume the question means |A+B|=|A-B| where A and B are non-zero vectors.

Squaring both sides,

|A+B|2=|A−B|2|A+B|2=|A−B|2

Since A.A=|A|2A.A=|A|2

|A+B|2=|A−B|2|A+B|2=|A−B|2

(A+B).(A+B)=(A−B).(A−B)(A+B).(A+B)=(A−B).(A−B)

A.A+A.B+B.A+B.B=A.A−A.B−B.A+B.BA.A+A.B+B.A+B.B=A.A−A.B−B.A+B.B( Using distributive property)

|A|2+2A.B+|B|2=|A|2−2A.B+|B|2|A|2+2A.B+|B|2=|A|2−2A.B+|B|2

4A.B=04A.B=0

A.B=0A.B=0

|A||B|cos(theta)=0|A||B|cos(theta)=0

Since A and B are non-zero vectors, A and B must be perpendicular as cos (90 degrees)=0


Anonymous: but ans is pie/2
Tamanna05: is it not
Tamanna05: π÷2=90°.
Answered by TheUnsungWarrior
1

Answer:

Angle, ∅= 120°

Explanation:

Given;-

          R = A + B

and,   R = A = B  ______(1)

Now, we know that when R = A = B;-

 ∵        R = 2A cos∅/2

 ∴        R = 2A cos 120°/2   [Putting ∅= 120 through trial and error method]

             R = 2A cos 60°

             R = 2A × 1/2  [since, cos 60°= 1/2]

             R = A  ______(2)

From, (1) and (2), we obtain;-

          R = A = B   [at ∅ = 120°]

Hope it helps ;-))

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