Trusted by Students Everywhere

Facebook

Why Choose Us?

0% AI Guarantee

Human-written only.

24/7 Support

Anytime, anywhere.

Plagiarism Free

100% Original.

Expert Tutors

Masters & PhDs.

100% Confidential

Your privacy matters.

On-Time Delivery

Never miss a deadline.

Find the vector, not with determinants, but by using properties of cross products

Math Jan 16, 2021

Find the vector, not with determinants, but by using properties of cross products. k times (i - 7j) Find the vector, not with determinants, but by using properties of cross products. (i + j) times (i - j) The figure shows a vector a the xy-plane and a vector b in the direction of k. Their lengths are Find |a times b|. Use the right-hand rule to decide whether the components of a times b are positive, negative x-component y-component z-component If a = (2, -1, 2) and b = (5, 2, 1), find the following. a times b = b times a =

Expert Solution

We recall the cross product property that

$i \times i =0, \ j \times j =0, \ k \times k =0,$

$i \times j =k, \ j \times k =i, \ k \times i =j,$

$j \times i =-k, \ k \times j =-i, \ i \times k =-j$

____________________________________________________________________________________

Answer: 1. We need to find $k \times (i -7j)$

$k \times (i -7j) = k\times i - 7(k\times j)$

$= -j -7(-i)$

$=\ {\color{Blue} 7i-1j+ 0k}$

__________________________________________________________________________________

Answer 2. Now we find $(i+j)\times (i-j)$

$(i+j)\times (i-j) = i\times (i-j) +j\times (i-j)$

$(i+j)\times (i-j) = i \times i- i \times j+j \times i-j \times j$

$(i+j)\times (i-j) = 0- k+(-k)-0$

$(i+j)\times (i-j) = {\color{Blue} - 2k}$

___________________________________________________________________________________

Answer 4. Given $a = \left \langle 2, -1, \ 2 \right \rangle$ and $b = \left \langle 5, \ 2, \ 1 \right \rangle$

$a\times b =\left \langle 2, \ -1, \ 2 \right \rangle \times \left \langle 5, \ 2, \ 1 \right \rangle$

Using distributive property and the properties of cross product

$a\times b =4 k -2j +5k -1i +10j -4i$

$a\times b ={\color{Blue} -5i +8j +9k}$

Now we find $b\times a$

$b\times a=\left \langle 5, \ 2, \ 1 \right \rangle \times \left \langle 2, \ -1, \ 2 \right \rangle$

$b\times a = -5k -10j -4k +4i +2j +1i$

$b\times a ={\color{Blue} 5i -8j -9k}$

_____________________________________________________________________________________

Archived Solution

Unlocked Solution

You have full access to this solution. To save a copy with all formatting and attachments, use the button below.

Already a member? Sign In

Important Note: This solution is from our archive and has been purchased by others. Submitting it as-is may trigger plagiarism detection. Use it for reference only.

For ready-to-submit work, please order a fresh solution below.

Or get 100% fresh solution

Get Custom Quote