Question

The sum of three vectors shown in the figure is 0.Find the magnitude of vectors OB and OC.​

Answer 1

Answer: OC = 5√2m and OB = 5m

Answer 2

Concept:

We can divide the vectors in components along x axis and y axis.

Given:

Magnitude of OA vector is 5m

Net resultant of all vectors is zero

OC vector make 45° angle with negative x axis.

Find:

Magnitude of vector OB

Magnitude of vector OC

Solution:

As the resultant given is zero

The resultant individually in x and y direction is zero

In Y direction

y component of OC should be equal to magnitude of OA to keep the resultant 0.

OC sin45° = OA

OC (1/√2) = 5

OC = 5√2

OC = 7.07 m

Magnitude of OC vector = 7.07 m

In X direction

y component of OC should be equal to magnitude of OB to keep the resultant 0.

OB = OC cos45°

OB = OC (1/√2)

OB = 7.07/√2

OB = 5 m

Magnitude of OB vector = 5 m

Hence the magnitude of Vector OC is 7.07 m and the magnitude of vector OB is 5 m.

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