Answer to Question #124278 in Algorithms for mochi

Question #124278
Calculate the dot product of a= (22, 2, 7) & b= (12, -9, 11). And Cross Product of c= (4, 0, 3) & d= (3, 1, 7).
1
Expert's answer
2020-07-01T06:31:27-0400

1) Use the component formula for the dot product of three-dimensional vectors


"\\bold{a\\cdot b}=a_1 b_1 +a_2 b_2+a_3b_3""\\bold{a\\cdot b}=22\\cdot 12+2\\cdot(-9)+7\\cdot 11=264-18+77=323"

2) Use the formula for the cross product of three-dimensional vectors


"\\bold{a\\times b}=\\begin{vmatrix}\n a_2 & a_3 \\\\\n b_2 & b_3\n\\end{vmatrix}\\bold{i}-\\begin{vmatrix}\n a_1 & a_3 \\\\\n b_1 & b_3\n\\end{vmatrix}\\bold{j}+\\begin{vmatrix}\n a_1 & a_2 \\\\\n b_1 & b_2\n\\end{vmatrix}\\bold{k}"

"\\bold{a\\times b}=\\begin{vmatrix}\n 2 & 7 \\\\\n -9 & 11\n\\end{vmatrix}\\bold{i}-\\begin{vmatrix}\n 22 & 7 \\\\\n 12 & 11\n\\end{vmatrix}\\bold{j}+\\begin{vmatrix}\n 22 & 2 \\\\\n 12 &-9\n\\end{vmatrix}\\bold{k}"

"\\bold{a\\times b}=(22+63)\\bold{i}-(242-84)\\bold{j}+(-198-24)\\bold{k}"

"\\bold{a\\times b}=85\\bold{i}-158\\bold{j}-222\\bold{k}"

"\\bold{a\\times b}=(85,-158,-222)"

Answer:

1) 323

2) (85,-158,-222)


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS