a cross b whole square
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a2 ×B2......is the answer
pandeyji26:
i have to prove a cross b whole sq is equal to mod a whole sq mod b whole sq minus a. b whole sq
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given: (a×b)²
to prove: (a×b)²= (a)²× (b)²- (a.b)²
Step-by-step explanation:
1. cross product is given by:
- a×b = mod(a)× mod(b)× sin(x)
2. dot product is given by:
a.b = mod(a)× mod(b)× cos(x)
squaring cross product written in (1), we get
(a×b)² = (mod(a)× mod(b)× sin(x))²
= (a)²× (b)²×sin²(x)
= (a)²× (b)²× (1-cos²(x))
= (a)²× (b)² - (a)²× (b)²× cos²(x)
(a×b)² = (a)²× (b)²- (a.b)²
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