Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our 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)

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.