Question

Perpendicular Vectors:
Find v x w if v=5i -4j +4k & w=-6i +3j -2k.
A. 3i-4j-2k
B. -14i-9j-4k
C. 5i +3j -4k
D. -4i -14j -9k

Find v x w if v=-3i-4j-8k & w=2i+6j+4k.
A. 12i -2j +3k
B. 8i +12j +32k
C. 32i -4j -10k
D. 10 i -8j +3k

Find the cross product <-6, 7, 2> x <8, 5, -3>. Is the resulting vector perpendicular to the given vectors?
A. <-31,-2,-86>;yes
B. <-37,-2,0>; no
C. <0,-86,-37>; yes
D. <-37, 0, -80>;no

Answer 1

D is the right answer for question #1. do you want the way how to get it?

Answer 2

Please

Answer 3

A is the right answer for #2

Answer 4

to find out the A x B (vector) you must write 3 coordinate in right line as
i, j, k
-6, 7 , 2 for vector A
8, 5 , -3 for vector B. (Don't forget AxB is not the same BxA)
for i term, you ignore the numbers below i, just count the leftover by diagonal line: that means counting 7 2
5 -3
7*(-3 )- 5*2 = -21-10 = -31it's for i
the same thing with j but, to j you must take - value. that means you count as above and then take negative value. the process is: ignore the numbers below the j, count the leftover by diagonal line. that means counting -6 2
8 -3
(-6)(-3) - 8*2 = 2 the result after counting is 2, take negative means -2 for j
for k term, do exactly what you do with i and j . Note that just jterm must be negative, i and k term take as they are
Hope this help. from now on, you can calculate whatever the 2 vectors are

Answer 5

I'm sorry, I typed them in line, but when posting they jump
7 2
5 -3 for i term

Answer 6

-6 2
8 -3 for j term

Answer 7

How do I know whether they are perpendicular or not?

Answer 8

do you know the dot product?

Answer 9

cross 2 vectors by the way i gave you is the way you find out the vector normal which is perpendicular to both 2 vectors. you have the formula to figure out whether they are perpendicular each other or not. It is : | A x B| = |A| *|B| sin (theta) . when you find out the vector AxB you can calculate |A xB| if |A xB| =0 they are parallel. and you know sin(90 degree) =1. right? you calculate | A x B|/ |A| *|B| if the result is 1, then they are perpendicular each other, if not, they are not perpendicular
hope this help