Question

TAKE HOME
1. Find the angle between the vectors:
i-23 + 5k and 3i+j - 2k

Answer 1

The angle between the two vectors

∝ = 64°

Explanation:

Step(i):-

Given that the vectors

`a^(-) = i^(-) - 2j^(-) +5k^(-)`

and

`b^(-) = 3i^(-) +j^(-) -2k^(-)`

`(a^(-) . b^(-) ) = (i^(-) - 2j^(-) +5k^(-) ) . (3 i^(-) + j^(-) - 2k^(-) )`

= 3 (i⁻ . i⁻) - 2(j⁻.j⁻) -10(k⁻.k⁻)

= 3 - 2 -10

= -9

Step(ii):-

Let '∝' be the angle between the two vectors

`cos\alpha = (a^(-).b^(-) )/(|a||b|)`

`cos\alpha = (|-9| )/(√(1+4+25)√(9+1+4) )`

`cos\alpha = (|-9| )/(√(30)√(14) )`

`\alpha =cos^(-1) ( (|-9| )/(√(30)√(14) ))`

∝ = cos⁻¹(0.4392) = 63.947

Final answer:-

The angle between the two vectors

∝ = cos⁻¹(0.4392) = 63.947

∝ = 64°