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Add vectors A ⃗,B ⃗ and C ⃗ each having magnitude of 100 unit and inclined to the X-axis at angles 45°, 135° and 315° respectively.

Add vectors A ⃗,B ⃗ and C ⃗ each having magnitude of 100 unit and inclined to the X-axis at angles 45°, 135° and 315° respectively.

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
9 years ago
Sol. x component of A ⃗ = 100 cos 45° = 100 / √2 unit x component of B ⃗ = 100 cos 135° = 100 / √2 x component of C ⃗ = 100 cos 315° 100 / √2 Resultant x component = 100 / √2 – 100 / √2 + 100/ √2 = 100 √2 Y component of A ⃗ = 100 sin 45° = 100 / √2 unit Y component of B ⃗ = 100 sin 135° = 100 / √2 Y component of C ⃗ = 100 sin 315° = 100 / √2 Resultant y component = 100 / √2 + 100 / √2 + 100 / √2 – 100 / √2 = 100 / √2 Resultant = 100 Tan α (y component )/(x component ) = 1 ⇒ α = tan-1 (1) = 45° The resultant is 100 unit at 45° with x-axis.

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