U=6k

V=-i+3j+k

What can i do here ?

U only have k

U=6k

V=-i+3j+k

What can i do here ?

U only have k

Tutors, please sign in to answer this question.

Westford, MA

Find the cross product and show it is orthogonal to both u and v.

u = 6k = <0,0,6>

v = -i + 3j + k = <-1,3,1>

u x v = 6k x (-i + 3j + k)

= -6(k x i) + 18(k x j) + 6(k x k)

= -6j + 18(-i) + 6(0)

= –18i – 6j = <-18,-6,0>

Orthogonal/perpendicular if dot product is 0:

(–18i – 6j) • (6k) = (-18)(0) + (-6)(0) + (0)(6) = 0

(–18i–6j) • (-i+3j+k) = (-18)(-1) + (-6)(3) + (0)(1) = 0

So the cross product u x v is orthogonal to u and v.

u = 6k = <0,0,6>

v = -i + 3j + k = <-1,3,1>

u x v = 6k x (-i + 3j + k)

= -6(k x i) + 18(k x j) + 6(k x k)

= -6j + 18(-i) + 6(0)

= –18i – 6j = <-18,-6,0>

Orthogonal/perpendicular if dot product is 0:

(–18i – 6j) • (6k) = (-18)(0) + (-6)(0) + (0)(6) = 0

(–18i–6j) • (-i+3j+k) = (-18)(-1) + (-6)(3) + (0)(1) = 0

So the cross product u x v is orthogonal to u and v.

Jane S.

Art Lessons for Adults, Teens and Middle School:Portfolio Prep

New York, NY

5.0
(75 ratings)

Faye L.

Regents Earth Science and Physical Science

Bronx, NY

5.0
(58 ratings)

- Math 9732
- Math Help 5396
- Word Problem 5060
- Algebra 5027
- Math Word Problem 4441
- Algebra 1 4035
- Algebra 2 3444
- Algebra Word Problem 2465
- Calculus 2189
- Chemistry 2185