explain law of parrallelogram of vector
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If two vectors acting simultaneously at a point can be represented both in magnitude and direction by the adjacent sides of a parallelogram drawn from a point, then the resultant vector is represented both in magnitude and direction by the diagonal of the parallelogram passing through that point.
let’s consider a slightly complex scenario. Imagine a boat in a river going from one bank to the other in a direction perpendicular to the flow of the river. This boat has two velocity vectors acting on it:
The velocity imparted to the boat by its engine
The velocity of the flow of the river.
When these two velocities simultaneously influence the boat, it starts moving with a different velocity. Let’s look at how we can calculate the resultant velocity of the boat.
To find the answer, let’s take two vectors a⃗ and b⃗ shown below, as the two adjacent sides of a parallelogram in their magnitude and direction.
Their sum, a⃗ + b⃗ is represented in magnitude and direction by the diagonal of the parallelogram through their common point. This is the Parallelogram law of vector addition.
Note: Using the Triangle law, we can conclude the following from Fig. 5
OA→ + AC→ = OC→ Or,
OA→ + OB→ = OC→ … since AC→ = OB→
Hence, we can conclude that the triangle and parallelogram laws of vector addition are equivalent to each other.
Plzz mark as Brainliest..
Hope this helps ..
If two vectors acting simultaneously at a point can be represented both in magnitude and direction by the adjacent sides of a parallelogram drawn from a point, then the resultant vector is represented both in magnitude and direction by the diagonal of the parallelogram passing through that point.
let’s consider a slightly complex scenario. Imagine a boat in a river going from one bank to the other in a direction perpendicular to the flow of the river. This boat has two velocity vectors acting on it:
The velocity imparted to the boat by its engine
The velocity of the flow of the river.
When these two velocities simultaneously influence the boat, it starts moving with a different velocity. Let’s look at how we can calculate the resultant velocity of the boat.
To find the answer, let’s take two vectors a⃗ and b⃗ shown below, as the two adjacent sides of a parallelogram in their magnitude and direction.
Their sum, a⃗ + b⃗ is represented in magnitude and direction by the diagonal of the parallelogram through their common point. This is the Parallelogram law of vector addition.
Note: Using the Triangle law, we can conclude the following from Fig. 5
OA→ + AC→ = OC→ Or,
OA→ + OB→ = OC→ … since AC→ = OB→
Hence, we can conclude that the triangle and parallelogram laws of vector addition are equivalent to each other.
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