Engineering Calculus Notes 103

Engineering Calculus Notes 103 - 91 1.6. CROSS PRODUCTS 5....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
1.6. CROSS PRODUCTS 91 5. Suppose that in ABC the vector from B to A is −→ v and that from B to C is −→ w . Use the vector formula for the distance from A to BC on p. 52 to prove that the area of the triangle is given by A ( ABC ) = 1 2 r ( −→ w · −→ w )( −→ v · −→ v ) ( −→ v · −→ w ) 2 . 6. Prove Proposition 1.6.2 . 7. Use Proposition 1.6.1 to prove Corollary 1.6.3 . ( Hint: If the rows are linearly dependent, what does this say about the parallelogram O PRQ ?) 8. Show that the cross product is: (a) skew-symmetric: −→ v × −→ w = −→ w × −→ v (b) additive in each slot: ( −→ v 1 + −→ v 2 ) × −→ w = ( −→ v 1 × −→ w ) + ( −→ v 2 × −→ w ) (use skew-symmetry to take care of the other slot: this is a kind of distributive law) (c) homogeneous in each slot:
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online