Answer to Question #307571 in Linear Algebra for Cynthia

Question

Question 1 of 12 7 Points

What follows is a calculated question with 14 blanks.

If a=⟨ 4,7,8 ⟩ and b=⟨ 5,10,2⟩ then:

|a|= Blank 15. Calculate the answer by read surrounding text.

|b|= Blank 16. Calculate the answer by read surrounding text.

a⋅b= Blank 17. Calculate the answer by read surrounding text.

a×b=⟨ Blank 18. Calculate the answer by read surrounding text.

, Blank 19. Calculate the answer by read surrounding text.

, Blank 20. Calculate the answer by read surrounding text.

⟩

b×a=⟨ Blank 21. Calculate the answer by read surrounding text.

, Blank 22. Calculate the answer by read surrounding text.

, Blank 23. Calculate the answer by read surrounding text.

⟩

a×a=⟨ Blank 24. Calculate the answer by read surrounding text.

, Blank 25. Calculate the answer by read surrounding text.

, Blank 26. Calculate the answer by read surrounding text.

⟩

The angle between a and b is Blank 27. Calculate the answer by read surrounding text.

Answer 1

Blank (15)

$\begin{array}{l} a = \left\langle {4,\,7,\,8} \right\rangle & , & b = \left\langle {5,\,10,\,2} \right\rangle \\ \\ \left| a \right| = \sqrt {{{\left( 4 \right)}^2} + {{\left( 7 \right)}^2} + {{\left( 8 \right)}^2}} \\ \\ \left| a \right| = \sqrt {16 + 49 + 64} = 129 \end{array}\$

Blank (16)

$\left| b \right| = \sqrt {{{\left( 5 \right)}^2} + {{\left( {10} \right)}^2} + {{\left( 2 \right)}^2}} \\ \left| b \right| = \sqrt {25 + 100 + 4} = 129$

Blank (17)

$\begin{array}{l} a = \left\langle {4,\,7,\,8} \right\rangle & , & b = \left\langle {5,\,10,\,2} \right\rangle \\ a\,\,b = \left\langle {4,\,7,\,8} \right\rangle \,\,\left\langle {5,\,10,\,2} \right\rangle \\ a\,\,b = \left( 4 \right)\left( 5 \right) + \left( 7 \right)\left( {10} \right) + \left( 8 \right)\left( 2 \right)\\ a\,\,b = 106 \end{array}\$

Blank (18, 19, 20)

Blank (21, 22, 23)

Blank (24, 25, 26)

Blank (27)

The angle between a and b is 

$\begin{array}{l} a \cdot b = \left| a \right|\left| b \right|\,\cos \theta \\ \theta = {\cos ^{ - 1}}\left( {\frac{{a \cdot b}}{{\left| a \right|\left| b \right|}}} \right)\\ \theta = {\cos ^{ - 1}}\left( {\frac{{106}}{{\sqrt {129} \sqrt {129} }}} \right)\\ \theta = {34.74^0} \end{array}\$