Question

calculate the dot product and the angle between the vectors:5i-2j+k and 2i-k​

Answer 1

Given:

Vector A = 5i-2j+k

Vector B = 2i-k​

To find:

The dot product of the two vectors and the angle between them.

Solution:

A·B= (5i-2j+k)· (2i-k)

= 5*2 + (-2)*0 + 1*(-1)

= 10 - 1 = 9

Magnitude of vector A = √(5²+(-2)²+1²)

= √(25+4+1) = √30

Magnitude of vector B = √(2²+(-1)²)

= √(4+1) = √5

Let the angle between the two vectors be ∅.

Then cos∅ = A·B/ |A||B|​

Putting the values:

cos∅ = 9/ √30√5

cos∅ = 9/ 5√6

∅= cos⁻¹ (9/ 5√6)

∅= cos⁻¹ (0.7348)

∅= 42.7°

Therefore the dot product between the two vectors is 9 and the angle between them is 42.7°.