Please help confirm if I got this problem correctly;
1)2jx(3i-4k)
sol>> 2x3jxi - 2x4jxk
= 6jxi - 8jxk
= 6k - 8i
2) (i-2j)xk
Solutn>> ixk - 2jxk
= -j - 2i
3) (2i-4k)x(ix2j)
solutn>>2ixi Please do help with this ONE
yes, correct.
On the third, break recheck if you typed it right. If the second parenthsis is i x 2j, then the answer is wrong.
4k-4j+8i
2ix2j=4k
2ix2j=4k
4k=4k
16k2=0
k2=0/16
k=0
In the third problem, it seems there is a mistake in the expression. The correct expansion should be:
(2i - 4k) x (i x 2j)
Let's simplify it step by step:
1) Distribute the scalar multiplication:
= 2i x (i x 2j) - 4k x (i x 2j)
2) Apply the scalar triple product identity:
= 2i x (2j x i) - 4k x (2j x i)
3) Use the vector cross product properties:
= 2i x (-2k) - 4k x (-2i)
4) Evaluate the cross products:
= (-2) * (2i x k) - (-2) * (4k x i)
5) Use the vector cross product properties:
= -4(i x k) - 8(k x i)
6) Swap the order in the cross products:
= -4(-j) - 8(-j)
7) Simplify the result:
= 4j - 8j
= -4j
So, the correct answer is -4j.
To confirm if the problem was solved correctly, let's go through each step of the solution:
3) (2i - 4k) × (ix2j)
First, simplify the expression inside the parentheses:
2i - 4k = (2i) - (4k) = 2i - 4k
Next, distribute the multiplication across each term:
(2i - 4k) × (ix2j) = (2i × i) - (4k × i) × (2j)
Now we can simplify further:
(2i × i) = 2i^2
Note: Recall that i × i = i^2
Then, we have:
- (4k × i) = -4ki
Finally, multiply -4ki by 2j:
-4ki × 2j = -8kij
Putting it all together:
(2i - 4k) × (ix2j) = 2i^2 - 8kij
So, the correct solution is 2i^2 - 8kij.