Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

a=5i+4j-6k ,b=-2i+2j+3k ,c=4i+3j+2k. find the vector perpendicular to a and c​

Sagot :

deriyan191293

Answer:

Explanation:

You can use the cross product. Let the vector that perpendicular to a and c is [tex]\vec{d}[/tex], so:

[tex]\vec{d}=\vec{a}\times\vec{c}=\left|\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\5&4&-6\\4&3&2\end{array}\right] \right|=(8+18)\hat{i}-\hat{j}(10+24)+\hat{k}(15-16)=26\hat{i}-34\hat{j}-\hat{k}[/tex]

To check that c is perpendicular with a and b, do the dot product between c and a and also c and b and if the result is zero, you're true.

[tex]\vec{d}.\vec{a}=(26*5)-(34*4)+(6)=0[/tex]  (c perpendicular to a)

[tex]\vec{d}.\vec{c}=(4*26)-(34*3)-(2*1)=0[/tex] (d perpendicular to c)

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.