Prove that (i) vector |a + b|^2 + vector |a + b|^2 = 2 vector { |a |^2 + |b |^2}

Question

Prove that

(i) vector |a + b|²+ vector |a + b|² = 2 vector { |a |² + |b |²}

(ii) vector |a + b|² - vector |a + b|² = 4 vector (a • b)

Monjur Alahi

7 views

2025-01-04 04:42

1 Answers

1 Answers 5 Views

1 Answers 7 Views

1 Answers 5 Views

1 Answers 4 Views

1 Answers 4 Views

1 Answers 4 Views

Define a null vector ( or Zero vector )

1 Answers 4 Views

1 Answers 8 Views

prove that, ∑ vector (a x ( b x c)) = 0

1 Answers 4 Views

1 Answers 4 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

consider,

vector |a + b|²+ vector |a + b|² = vector {|a|² + 2 a • b + | b |²} + vector {| a |² - 2 a • b + |b|²}

= 2 vector { | a |² + | b |² }

Next consider,

vector | a + b |²- vector | a + b |²= vector { | a |² + 2 a • b + | b |² } - vector { | a |² - 2 a • b + | b |² }

= 4 vector (a • b)