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Let a ⃗=2i ⃗+3j ⃗+4k ⃗ and b ⃗=3i ⃗+4j ⃗+5k ⃗. Find the angle between them .

Let a ⃗=2i ⃗+3j ⃗+4k ⃗ and b ⃗=3i ⃗+4j ⃗+5k ⃗. Find the angle between them .

Grade:10

1 Answers

Jitender Pal
askIITians Faculty 365 Points
9 years ago
Sol. a ⃗ = 2i ⃗ + 3 j ⃗ + 4k ⃗; b ⃗ = 3i ⃗ + 4 j ⃗ + 5k ⃗ a ⃗ . b ⃗ = ab cos θ ⇒ θ = cos-1 (a ⃗ .b ⃗)/ab ⇒ cos-1 ( 2 x 3+3 x 4 +4 x 5)/(√(2^2 +3^2+4^2 ) √(3^2+4^2+5^2 )) = cos-1 (38/√1450)

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