Chapter 10: Q. 4 (page 823)
How is the determinant of a 3 × 3 matrix used in the computation of the determinant of two vectors?
Short Answer
The determinant of a 3 × 3 matrix is .
Chapter 10: Q. 4 (page 823)
How is the determinant of a 3 × 3 matrix used in the computation of the determinant of two vectors?
The determinant of a 3 × 3 matrix is .
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Get started for freeIn Exercises 36–41 use the given sets of points to find:
(a) A nonzero vector N perpendicular to the plane determined by the points.
(b) Two unit vectors perpendicular to the plane determined by the points.
(c) The area of the triangle determined by the points.
(Hint: Think of the -plane as part of .)
Find
A function f that satisfies the hypotheses of Rolle’s Theorem on [−2, 2] and for which there are exactly three values c ∈ (−2, 2) that satisfy the conclusion of the theorem .
Give an example of three vectors in that form a right-handed triple. Explain how you can use the same three vectors to form a left-handed triple.
Suppose that we know the reciprocal rule for limits: If exists and is nonzero, then This limit rule is tedious to prove and we do not include it here. Use the reciprocal rule and the product rule for limits to prove the quotient rule for limits.
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