I do not understand how to work out this product and i would like some help please!
Two vectors u and v are such that ∥u∥=11, ∥v∥=8 and u⋅v=−2.
Using propertes of the dot product, find (2u+4v)⋅(6u−9v).
Two vectors u and v are such that ∥u∥=11, ∥v∥=8 and u⋅v=−2.
Using propertes of the dot product, find (2u+4v)⋅(6u−9v).
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(2u + 4v) ⋅ (6u − 9v)
= (2u) ⋅ (6u − 9v) + (4v) ⋅ (6u − 9v)
= [(2u) ⋅ (6u)] + [(2u) ⋅ (−9v)] + [(4v) ⋅ (6u)] + [(4v) ⋅ (−9v)]
= 12(u ⋅ u) - 18(u ⋅ v) + 24(v ⋅ u) - 36(v ⋅ v)
= 12(u ⋅ u) - 18(u ⋅ v) + 24(u ⋅ v) - 36(v ⋅ v)
= 12(u ⋅ u) + 6(u ⋅ v) - 36(v ⋅ v)
= 12∥u∥² + 6(u ⋅ v) - 36∥v∥²
= 12(11)² + 6(-2) - 36(8)²
= -864
= (2u) ⋅ (6u − 9v) + (4v) ⋅ (6u − 9v)
= [(2u) ⋅ (6u)] + [(2u) ⋅ (−9v)] + [(4v) ⋅ (6u)] + [(4v) ⋅ (−9v)]
= 12(u ⋅ u) - 18(u ⋅ v) + 24(v ⋅ u) - 36(v ⋅ v)
= 12(u ⋅ u) - 18(u ⋅ v) + 24(u ⋅ v) - 36(v ⋅ v)
= 12(u ⋅ u) + 6(u ⋅ v) - 36(v ⋅ v)
= 12∥u∥² + 6(u ⋅ v) - 36∥v∥²
= 12(11)² + 6(-2) - 36(8)²
= -864
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The problem tell you exactly what to do !!!!!!!!!!!!!!!
(2u+4v)⋅(6u−9v) = 12u^2 - 18u⋅v +24u⋅v - ..... Don't you know how to take a dot product?
(2u+4v)⋅(6u−9v) = 12u^2 - 18u⋅v +24u⋅v - ..... Don't you know how to take a dot product?