Two vectors vector a and vector b,is a vector + b vector and a vector - b vector same ?
Answers
Answer:
Hint: Dot product of two perpendicular vector is zero.
Step 1: Calculation of resultant of
A
and
B
Since
∣
A
+
B
∣=
2
1
∣
B
∣ [Given]
∣
R
∣=∣
A
+
B
∣=
A
2
+B
2
+2ABcosθ
∴
A
2
+B
2
+2ABcosθ
=
2
1
B
Squaring both sides
A
2
+B
2
+2ABcosθ=
4
B
2
⇒ A
2
+2ABcosθ−
4
3
B
2
=0 ....(1)
Step 2: Take dot product between
R
and
A
R
⊥ to
A
∴ We can say that
A
⋅(
A
+
B
)=0
⇒
A
⋅
A
+
A
⋅
B
=0
⇒ A
2
+ABcosθ=0 ....(2)
Step 3: Solving the equations
From eqn (1) and (2)
A
2
−2A
2
+
4
3
B
2
=0
⇒ A
2
=
4
3
B
2
⇒ A=
2
3
B
From step (2)
Now, cosθ=−
B
A
=
2
−
3
B
B
⇒ cosθ=
2
−
3
⇒ θ=150
∘