1.Find vectors v*w if vector v = 5 vector i – 4 vector j + 4 vector k and vector w = –6 vector i + 3 vector j – 2 vector k.
2.Find vectors v*w if vector v = -3 vector i – 4 vector j - 8 vector k and vector w = 2 vector i + 6 vector j + 4 vector k.
v*w has no meaning in common notation.
Do you mean v•w or v×w ?
v times w
i assume you mean cross-product
I'll do #1:
vxw =
| i j k|
|5 -4 4 |
|-6 3 -2|
= 32i-28j+26k
You can make things a lot more readable by just saying you're dealing with vectors. Then you can forget about all those words and just write the values, as in my answer.
no i don't mean cross product.
3– 4– 2
–14– 9– 4
5+ 3– 4
–4– 14– 9
these are the possible answers. all with IJK following of course.
In that case, say dot product.
5i-4j+4k • -5i+3j-2k = -25-12-8 = -45
you say you don't mean cross product, but you give vectors for answers.
dot product of two vectors is just a number.
I'm afraid I don't know what operation you are using.
To find the vector product (also known as the cross product) of two vectors, v and w, we can use the following formula:
v * w = (v_y*w_z - v_z*w_y) * i + (v_z*w_x - v_x*w_z) * j + (v_x*w_y - v_y*w_x) * k
Let's calculate the vector product of the given vectors:
1. For vector v = 5i - 4j + 4k and vector w = -6i + 3j - 2k:
v * w = ((-4 * -2) - (4 * 3)) * i + ((4 * -6) - (5 * -2)) * j + ((5 * 3) - (-4 * -6)) * k
= (-8 - 12) * i + (-24 + 10) * j + (15 + 24) * k
= -20i - 14j + 39k
So, v * w = -20i - 14j + 39k.
2. For vector v = -3i - 4j - 8k and vector w = 2i + 6j + 4k:
v * w = ((-4 * 4) - (-8 * 6)) * i + ((-8 * 2) - (-3 * 4)) * j + ((-3 * 6) - (-4 * 2)) * k
= (-16 + 48) * i + (-16 - 12) * j + (-18 + 8) * k
= 32i - 28j - 10k
So, v * w = 32i - 28j - 10k.
Therefore, the vector product of the given vectors are:
1. v * w = -20i - 14j + 39k.
2. v * w = 32i - 28j - 10k.