Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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Find the cross product a x b.
a =j+ 6k, b = 2i -j + 5k
Verify that it is orthogonal to both a and b.
(a x b) a =
(a x b) b =
Find the cross product a x b.
a = j + 6k,
b = 31 - j+ 2k
Verify that it is orthogonal to both a and b.
(a x b) · a =
(a x b) · b =
Find the cross product a x b.
a = (2, 5, 0), b = (1, 0, 3)
Verify that it is orthogonal to both a and b.
(a x b) a =
(a x b) b =
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- Find the cross product a × b. a = i − j − k, b = 1/2 i + j + 1/5 k Verify that it is orthogonal to both a and b. (a × b) · a = (a × b) · b =arrow_forwardFind the cross product a × b. a-i-j-k, b-tj+* Verify that it is orthogonal to both a and b. (a x b) - a = (a × b) · b = %3Darrow_forwardFind the cross product ⃗a × b and then specifically verify that it is orthogonal to both ⃗a and b: ⃗a = ⟨6, 0, −2⟩ And ⟨0, 8, 0⟩arrow_forward
- (3) Show that (u - v) × (u + v) = 2(u × v).arrow_forwardCalculate the triple scalar products w. (v × u) and u ⋅ (w × v), where u = (7, 2, −1), v = w. (vx u) = 330 = (2, 8, -3), and w = u. (w x v) = 350 = (9, 8, -10).arrow_forwardCalculate the cross product assuming that u x v = (4, 3, 0). v x (u + v)arrow_forward
- Assume that v lies in the yz-plane. Which of the following dot products is equal to zero for all choices of v? (a) v. (0, 2, 1) (b) v · k (c) v · (-3, 0, 0) (d) v ·jarrow_forwardFor any two vectors u and v use the definition of the cross product in coordinatesto prove that u × v + v × u = 0.arrow_forwardFind the value of β for which w =〈−2, β〉 is parallel to v =〈4, −3〉.arrow_forward
- Find the cross product a x b. a = (t, 8, 1/t), b = (12, t², 1) Verify that it is orthogonal to both a and b. (a x b) · a = (a x b) · b = Need Help? Read It Watch Itarrow_forwardUse the geometric definition of the cross product and the properties of the cross product to make the following calculations. (a) ((j + k) × j) × k = (b) (i + j) × (i × j) = (c) 3k × (k + j) = (d) (i + j) × (i − j) = -arrow_forwardA good check on a cross product calculation is to verify that u and v are orthogonal to the computed u × v. verify that u ⋅ (u × v) = 0 and v ⋅ (u × v) = 0.arrow_forward
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