Question

The line of the angle between the vectors à = 3î +j+k, b= 2î - 2j+k is​

Answer 1

EXPLANATION.

Angle between the vectors.

⇒ a = 3i + j + k.

⇒ b = 2i - 2j + k.

As we know that,

⇒ | a | = √(3)² + (1)² + (1)².

⇒ | a | = √9 + 1 + 1.

⇒ | a | = √11.

⇒ | b | = √(2)² + (-2)² + (1)².

⇒ | b | = √4 + 4 + 1.

⇒ | b | = √9.

⇒ | b | = 3.

⇒ (a . b) = (3i + j + k).(2i - 2j + k).

⇒ (a . b) = 6 - 2 + 1.

⇒ (a . b) = 5.

As we know that,

Angle between two vectors.

⇒ cosθ = a . b/| a | | b |.

⇒ cosθ = 5/3√11.

                                                                                                                       

MORE INFORMATION.

Properties of scalar products.

(1) = (a . b) . b is not defined.

(2) = (a + b)² = a² + 2 a. b + b².

(3) = (a - b)² = a² - 2 a. b + b².

(4) = (a + b).(a - b) = a² - b².

(5) = | a + b | = |a| + |b| = a ║ b.

(6) = | a + b |² = |a|² + |b|² = a ⊥ b.

(7) = | a + b| = |a - b| = a ⊥ b.