find the triple product of (A*B).C given that A =i + 4j, B=2i - 3j and C = i + k?
Recall that A•B×C =
|a1 a2 a3|
|b1 b2 b3|
|c1 c2 c3|
Now, since u•v = v•u, A×B•C = C•A×B =
|1 0 1|
|1 4 0| = -11
|2 -3 0|
To find the triple product of (A*B).C, we first need to calculate the dot product of A and B, and then take the dot product of the result with C.
Step 1: Calculate the dot product of A and B:
The dot product of two vectors A = (A1, A2) and B = (B1, B2) is given by:
A.B = A1 * B1 + A2 * B2
Given A = i + 4j and B = 2i - 3j:
A.B = (1 * 2) + (4 * -3)
= 2 - 12
= -10
Step 2: Take the dot product of the result with C:
Given C = i + k, where k is a constant:
(A*B).C = (-10) * (1) + (-10) * k
= -10 - 10k
So, the triple product of (A*B).C is given by -10 - 10k.