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22. Show that (a X b) b = 0 for all vectors a and b in V₁.

22. Show that (a X b) b = 0 for all vectors a and b in V₁.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Solve question 22 only!
16. The figure shows a vector a in the xy-plane and a vector b in the direction of k. Their lengths are |a|-3 and | b|-2. (a) Find a x b. (b) Use the right-hand rule to decide whether the components of a xb are positive, negative, or 0. A 17. If a = (2, -1, 3) and b = (4, 2, 1), find a × b and b x a. 18. If a = (1, 0, 1), b = (2, 1, -1), and c = (0, 1, 3), show that a X (b X c) = (a × b) X c. 19. Find two unit vectors orthogonal to both (3, 2, 1) and (-1, 1, 0). 20. Find two unit vectors orthogonal to both j - k and i + j. 21. Show that 0 Xa=0= a × 0 for any vector a in V₁. 22. Show that (a × b) · b −0 for all vectors a and b in V₁.
Transcribed Image Text:16. The figure shows a vector a in the xy-plane and a vector b in the direction of k. Their lengths are |a|-3 and | b|-2. (a) Find a x b. (b) Use the right-hand rule to decide whether the components of a xb are positive, negative, or 0. A 17. If a = (2, -1, 3) and b = (4, 2, 1), find a × b and b x a. 18. If a = (1, 0, 1), b = (2, 1, -1), and c = (0, 1, 3), show that a X (b X c) = (a × b) X c. 19. Find two unit vectors orthogonal to both (3, 2, 1) and (-1, 1, 0). 20. Find two unit vectors orthogonal to both j - k and i + j. 21. Show that 0 Xa=0= a × 0 for any vector a in V₁. 22. Show that (a × b) · b −0 for all vectors a and b in V₁.
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