if the max & min resultants of thetwo vectols ae 7 & 1 respectively.find the resultant when they areacting at right angles to eachother
Answers
Answer:
Correct option is
D
13
Step 1: Equation for resultant of two vectors
Let θ be the angle between the vectors
A
and
B
The resultant of two vectors is given by
R=
A
2
+B
2
+2ABcosθ
For R
max
,θ=0
∘
⇒∣
R
max
∣=∣
A
∣+∣
B
∣
⇒17=∣
A
∣+∣
B
∣ ....(1)
For R
min
,θ=180
∘
⇒∣
R
min
∣=∣
A
∣−∣
B
∣
⇒7=∣
A
∣−∣
B
∣ ....(2)
Step 2: Calculation of Magnitude of
A
and
B
Adding equation (1) and (2) ⇒2∣
A
∣=24
⇒
A
=12
From equation (1)⇒ ∣
B
∣=5
Step 3: Calculation of R when vectors are perpendicular
∵
A
⊥
B
∣
R
∣=
A
2
+B
2
+2ABcos90
o
⇒∣
R
∣=
12
2
+5
2
=
169
units
⇒∣
R
∣=13 units
Hence the magnitude of resultant vector is 13 units. Option D is correct.