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1) Select True or False. Given non-zero vectors a,b,c eV, and keR.. is the dot product and x is the cross product. "Meaningful" means the operation(s) can be performed with the given quantities. No explanation necessary. (a) True/False: The expression k(b×č) is meaningful. (b) True/False: The expression (ā·b)+(ã+b) is meaningful. (c) True/False: In R³, two planes perpendicular to a third plane are perpendicular. (d) True/False: For two vectors ā and b, |a+b||-|à|≤|b| (e) True/False: The vector (4,-1,2) is orthogonal to the plane -8x-2y+4z=7.

1) Select True or False. Given non-zero vectors a,b,c eV, and keR.. is the dot product and x is the cross product. "Meaningful" means the operation(s) can be performed with the given quantities. No explanation necessary. (a) True/False: The expression k(b×č) is meaningful. (b) True/False: The expression (ā·b)+(ã+b) is meaningful. (c) True/False: In R³, two planes perpendicular to a third plane are perpendicular. (d) True/False: For two vectors ā and b, |a+b||-|à|≤|b| (e) True/False: The vector (4,-1,2) is orthogonal to the plane -8x-2y+4z=7.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 11E
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1) 2) Select True or False. Given non-zero vectors a,b,c € V₂ and keR.. is the dot product and × is the cross product. "Meaningful" means the operation(s) can be performed with the given quantities. No explanation necessary. (a) True/False: The expression k(b×č) is meaningful. (b) True/False: The expression (ā·b)+(ã+b) is meaningful. (c) True/False: In R³, two planes perpendicular to a third plane are perpendicular. (d) True/False: For two vectors ā and b, ||ã+b||-|ā|≤|b| (e) True/False: The vector (4,-1,2) is orthogonal to the plane -8x-2y+4z=7. Describe in words and sketch the following surface, in the 3-dimensional coordinate system. Use the standard orientation for the axes, with the positive z-axis pointing up. Show work. x² + y² +z²-6y+2z = 4
Transcribed Image Text:1) 2) Select True or False. Given non-zero vectors a,b,c € V₂ and keR.. is the dot product and × is the cross product. "Meaningful" means the operation(s) can be performed with the given quantities. No explanation necessary. (a) True/False: The expression k(b×č) is meaningful. (b) True/False: The expression (ā·b)+(ã+b) is meaningful. (c) True/False: In R³, two planes perpendicular to a third plane are perpendicular. (d) True/False: For two vectors ā and b, ||ã+b||-|ā|≤|b| (e) True/False: The vector (4,-1,2) is orthogonal to the plane -8x-2y+4z=7. Describe in words and sketch the following surface, in the 3-dimensional coordinate system. Use the standard orientation for the axes, with the positive z-axis pointing up. Show work. x² + y² +z²-6y+2z = 4
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