(a) Explanation Given information: Vectors u and v have same magnitude. Formula used: Two vectors v and w are orthogonal if and only if v ⋅ w = 0 . Proof: Consider, ( u + v ) ⋅ ( u − v ) ⇒ ( u + v ) ⋅ ( u − v ) = u ⋅ ( u − v ) + v ⋅ ( u − v ) ⇒ ( u + v ) ⋅ ( u − v ) = u ⋅ u − u ⋅ v + v ⋅ u − v ⋅ v ⇒ ( u + v ) & (b) To determine To prove: The angle inscribed in a semicircle shown below is a right angle where u + v and u − v are orthogonal.

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Chapter 8.5, Problem 43AYU

(a)

To determine

To prove: $u+v$ and $u−v$ are orthogonal, if $u$ and $v$ have same magnitude.

(b)

To determine

To prove: The angle inscribed in a semicircle shown below is a right angle where $u+v$ and $u−v$ are orthogonal.

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Chapter 8.5, Problem 46AYU

Chapter 8.5, Problem 47AYU

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Chapter 8 Solutions

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To prove: u + v and u − v are orthogonal, if u and v have same magnitude.

Solution Summary: The author explains that two vectors u and v are orthogonal if they have the same magnitude.

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To prove: $u+v$ and $u−v$ are orthogonal, if $u$ and $v$ have same magnitude.

To prove: The angle inscribed in a semicircle shown below is a right angle where $u+v$ and $u−v$ are orthogonal.

Want to see the full answer?

Chapter 8 Solutions

To prove: u + v and u − v are orthogonal, if u and v have same magnitude.

Solution Summary: The author explains that two vectors u and v are orthogonal if they have the same magnitude.

Videos

To prove: u+v<m:math><m:mrow><m:mi>u</m:mi><m:mo>+</m:mo><m:mi>v</m:mi></m:mrow></m:math> and u−v<m:math><m:mrow><m:mi>u</m:mi><m:mo>−</m:mo><m:mi>v</m:mi></m:mrow></m:math> are orthogonal, if u<m:math><m:mi>u</m:mi></m:math> and v<m:math><m:mi>v</m:mi></m:math> have same magnitude.

To prove: The angle inscribed in a semicircle shown below is a right angle where u+v<m:math><m:mrow><m:mi>u</m:mi><m:mo>+</m:mo><m:mi>v</m:mi></m:mrow></m:math> and u−v<m:math><m:mrow><m:mi>u</m:mi><m:mo>−</m:mo><m:mi>v</m:mi></m:mrow></m:math> are orthogonal.

Want to see the full answer?

Chapter 8 Solutions

To prove: $u+v$ and $u−v$ are orthogonal, if $u$ and $v$ have same magnitude.

To prove: The angle inscribed in a semicircle shown below is a right angle where $u+v$ and $u−v$ are orthogonal.