Refer to reading text for information.Students will compare and contrast two sculptural depictions of the biblical narrative of David and Goliath. This process will involve research and analysis in de
Name: ___________________ Math 2101 – Linear Algebra
Homework 6 20 points
Put answers in spaces provided. Please use pencil. Show work.
If 
is the length of vector 
, the normalized vector that corresponds to is 
. Find the normalized vectors that correspond to the given vectors, but do not have square roots in the denominators of the vector entries. (6 points total)
Normalized vector corresponding to 
[ _____ _____ _____ ].
Normalized vector corresponding to 
[ _____ _____ _____ ].
Normalized vector corresponding to 
[ _____ _____ _____ ].
If 
, then the vectors 
have length 1. If the four numbers do not have a common factor greater than 1, then d must be odd. For the given values if d, find a, b and c, where all three numbers are non-zero. (6 points total)
If d = 17, an all positive valued rational unit vector with denominator 17 is 
.
If d = 13, an all positive valued rational unit vector with denominator 13 is 
.
If d = 11, an all positive valued rational unit vector with denominator 11 is 
.
(continued on back)
Let 
[a b c] and 
[d e f] be linearly independent 3 dimensional vectors. The cross product 
is a new vector orthogonal to both 
. If the original two vectors are orthogonal to each other, the length of the cross product is equal to the lengths of the original vectors multiplied together. This means if we have two orthonormal three dimensional vectors, the cross product will give us the third orthonormal vector for a basis for three dimensional space. Find the cross products of the following vectors, written as fractions in lowest terms. (8 points total)
and 
and 
and 
and 
