Tamil Nadu Board of Secondary EducationHSC Science Class 11

Calculate the area of the triangle for which two of its sides are given by the vectors A→=5i^-3j^,B→=4i^+6j^ - Physics

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Sum

Calculate the area of the triangle for which two of its sides are given by the vectors `vecA = 5hati - 3hatj, vecB = 4hati + 6hatj`

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Solution

Area of the triangle = `1/2 |vecA xx vecA|`

`overlineA xx overlineB = |[hati, hatj, hatk], [5, -5, 0], [4, 6, 0]| = hati(0) + hatj(0) + hatk(30 + 12) = 42hatk`

`|overlineA xx overlineB| = sqrt(42^2) = 42`

∴ Area of the triangle = `1/2|overlineA xx overlineB| = 1/2 xx 42 = 21` m2

Concept: Elementary Concept of Vector Algebra
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Chapter 2: Kinematics - Evaluation [Page 102]

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