Question

Tính góc giữa hai véc tơ a,b trong các trường hợp sau

a) véc tơ a = (3,-4), véc tơ b = (4,3)

b) véc tơ a = (2,5), véc tơ b = (3,-7)

c) véc tơ a = (2,-3), véc tơ b = (6,4)

d) véc tơ a = (3,2), véc tơ b = (5,-1)

Answer 1

a.

\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\frac{\overrightarrow{a}.\overrightarrow{b}}{\left|\overrightarrow{a}\right|.\left|\overrightarrow{b}\right|}=\frac{3.4-4.3}{\left|\overrightarrow{a}\right|.\left|\overrightarrow{b}\right|}=0\)

\(\Rightarrow\left(\overrightarrow{a};\overrightarrow{b}\right)=90^0\)

b.

\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\frac{\overrightarrow{a}.\overrightarrow{b}}{\left|\overrightarrow{a}\right|.\left|\overrightarrow{b}\right|}=\frac{2.3-5.7}{\sqrt{2^2+5^2}.\sqrt{3^2+\left(-7\right)^2}}=-\frac{\sqrt{2}}{2}\)

\(\Rightarrow\left(\overrightarrow{a};\overrightarrow{b}\right)=135^0\)

c.

\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\frac{2.6-3.4}{\left|\overrightarrow{a}\right|.\left|\overrightarrow{b}\right|}=0\Rightarrow\left(\overrightarrow{a};\overrightarrow{b}\right)=90^0\)

d.

\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\frac{3.5-2.1}{\sqrt{3^2+2^2}.\sqrt{5^2+\left(-1\right)^2}}=\frac{\sqrt{2}}{2}\)

\(\Rightarrow\left(\overrightarrow{a};\overrightarrow{b}\right)=45^0\)