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IBMathsDPApplications & Interpretation (AI)HLRevision Notes3. Geometry & TrigonometryVector PropertiesAreas using the Vector Product

Areas using the Vector Product (DP IB Applications & Interpretation (AI)): Revision Note

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Areas using Vector Product

How do I use the vector product to find the area of a parallelogram?

  • The area of the parallelogram with two adjacent sides formed by the vectors v and w is equal to the magnitude of the vector product of two vectors v and w

    • A equals open vertical bar bold italic v blank cross times blank bold italic w close vertical bar blankwhere v and w form two adjacent sides of the parallelogram

      • This is given in the formula booklet

 

How do I use the vector product to find the area of a triangle?

  • The area of the triangle with two sides formed by the vectors v and w is equal to half of the magnitude of the vector product of two vectors v and w

    • A equals 1 half open vertical bar bold italic v blank cross times blank bold italic w close vertical bar blankwhere v and w form two sides of the triangle

      • This is not given in the formula booklet

Examiner Tips and Tricks

  • The formula for the area of the parallelogram is given in the formula booklet but the formula for a triangle is not

    • Remember that the area of a triangle is half the area of a parallelogram

Worked Example

Find the area of the triangle enclosed by the coordinates (1, 0, 5), (3, -1, 2) and (2, 0, -1).

3-10-4-ib-aa-hl-area-we-solution

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