Calculate the angle between two vectors

Geometry Level 3

If a ⃗ = 2 i ⃗ + j ⃗ \vec{a}=2\vec{i}+\vec{j} and b ⃗ = 4 i ⃗ − 2 j ⃗ \vec{b}=4\vec{i}-2\vec{j} calculate the angle formed by both vectors.Remember:the cosine of the angle is the scalar multiplication of the vectors divided by the multiplication of the vectors modules.

13.5 180 53.13 None of them 90

∆Lex Palacin by ∆lex Palacin , 32, Spain

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Parth Sankhe
Oct 15, 2018

cos ⁡ θ = a ⋅ b ∣ a ∣ × ∣ b ∣ \cos \theta =\frac { a \cdot b}{|a| × |b|}

= 2 × 4 + 1 × ( − 2 ) √ 5 ⋅ √ 20 \frac {2×4 + 1×(-2)}{√5 \cdot √20}

= 3 5 \frac {3}{5}

Therefore, θ = cos ⁡ − 1 3 5 = 53.13 ° \theta = \cos^{-1}\frac {3}{5}=53.13°

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...