Answer:
A
Step-by-step explanation:
Given
u = <6, -1>
u = 6i-j
and
v=<7,-4>
v=7i-4j
The formula for angle is:
Let x be the angle
[tex]cos\ x = \frac{u.v}{||u||.||v||}[/tex]
where ||u|| is the length and u.v is the dot product or scalar product of both vectors
So,
[tex]||u|| = \sqrt{(6)^2+(-1)^2}\\ = \sqrt{36+1}\\ = \sqrt{37}\\ ||v||=\sqrt{(7)^2+(-4)^2}\\ = \sqrt{49+16}\\ = \sqrt{65}\\[/tex]
[tex]u.v = u_1u_2+v_1v_2\\= (6)(7)+(-1)(-4)\\=42+4\\=46[/tex]
[tex]cos\ x=\frac{46}{\sqrt{37}\sqrt{65}} \\= \frac{46}{\sqrt{2405} }\\Can\ also\ be\ written\ as:\\= \frac{46}{\sqrt{2405} } * \frac{\sqrt{2405} }{\sqrt{2405}} \\=\frac{46\sqrt{2405} }{2405}[/tex]
The calculated angle will be in radians. To find the angle in degrees:
[tex]x = \frac{180}{\pi} cos^{-1} (\frac{46\sqrt{2405} }{2405})\\x = 20.282\\x= 20.3\\[/tex]
Hence Option A is correct ..
