Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Answer:
The acute angle lies between the vectors a=3i+4j and b=7i+j is 45°
Explanation:The given vectors are:
a = 3i + 4j
b = 7i + j
The acute angle between vectors a and and b is given by the formula:
[tex]\theta=\cos ^{-1}\frac{a.b}{|a\mleft\Vert b\mright|}[/tex]The scalar product of vectors a and b is:
a.b = (3i + 4j).(7i + j)
a.b = (3x7) + (4x1)
a.b = 21 + 4
a.b = 25
The magnitude of a is:
[tex]\begin{gathered} |a|=\sqrt[]{3^2+4^2} \\ |a|=\sqrt[]{9+16} \\ |a|=\sqrt[]{25} \\ |a|=5 \end{gathered}[/tex]The magnitude of b is:
[tex]\begin{gathered} |b|=\sqrt[]{7^2+1^2} \\ |b|=\sqrt[]{49+1} \\ |b|=\sqrt[]{50} \\ |b|=5\sqrt[]{2} \end{gathered}[/tex]Substituting the values of a.b, |a|, and |b| into the formula for the acute angle.
[tex]\begin{gathered} \theta=\cos ^{-1}\frac{a.b}{|a\Vert b|} \\ \theta=\cos ^{-1}\frac{25}{5\times5\sqrt[]{2}} \\ \theta=\cos ^{-1}\frac{25}{25\sqrt[]{2}} \\ \theta=\cos ^{-1}\frac{1}{\sqrt[]{2}} \\ \theta=45^0 \end{gathered}[/tex]Therefore, the acute angle lies between the vectors a=3i+4j and b=7i+j is 45°
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
