Given vectors A= (Axi + Ayj), B= (Byj+Bzk) and C= (Cyj + Czk).
a) find the triple product of these vectors defined by A dot (BxC) in terms of the vector components.
I get 0 as the answer.
b) is the result found in a) a scalar of a vector?
since I had to multiply finally by the scalar product, the answer in a is scalar.
Am I right?
Well, looking at BxC, jxj is zero, jxz is i, kxj is minus i, and kxk is zero.
BxC is By*Cz (i) + Bz x Cy (-i)
Dotting that with Axi hardly gives zero. Check my work, I did it in my head.
dot products always gives scalars.
To find the triple product of these vectors defined by A dot (BxC), we can follow these steps:
Step 1: Calculate BxC:
To calculate BxC, you need to take the cross product of B and C. The cross product between two vectors in three dimensions can be determined using the determinant method or by calculating the individual components.
BxC = (By*Cz)i + (Bz*Cx)j + (-By*Cx)k
Simplifying this further, we have:
BxC = By*Cz(i) + Bz*Cx(j) - By*Cx(k)
Step 2: Take the dot product of A with BxC:
To find the dot product of A with BxC, you need to multiply the corresponding components of A and BxC and sum them up.
A dot (BxC) = Axi*(By*Cz) + Ayj*(Bz*Cx) + Azk*(-By*Cx)
Simplifying this further, we have:
A dot (BxC) = Axi*By*Cz + Ayj*Bz*Cx - Azk*By*Cx
Based on the information given in the question, where A = (Axi + Ayj), B = (Byj + Bzk), and C = (Cyj + Czk), let's substitute the values into the equation:
A dot (BxC) = Axi*By*Cz + Ayj*Bz*Cx - Azk*By*Cx
= Axi*By*0 + Ayj*0*Cx - Azk*By*Cx
= 0
Therefore, the triple product A dot (BxC) equals zero.
As for part (b) of your question, you are correct. The result obtained in part (a), which is zero, is a scalar. Dot products always yield scalars, not vectors.