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Question

(a×b).c=a(b×c)

A
True
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B
False
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Solution

The correct option is A True
Let
a=a1ˆi+a2ˆj+a3ˆk
b=b1ˆi+b2ˆj+b3ˆk
c=c1ˆi+c2ˆj+c3ˆk
(a×b).c Isn’t it scalar triple product of a,bandc?
= =∣ ∣a1a2a3b1b2b3c1c2c3∣ ∣
Now a.(b×c) can be written as (b×c).a (Dot product is commutative).
Now (b×c).a is again a scalar triple product given by ∣ ∣b1b2b3c1c2c3a1a2a3∣ ∣
Now ∣ ∣b1b2b3c1c2c3a1a2a3∣ ∣ =∣ ∣a1a2a3b1b2b3c1c2c3∣ ∣ why?
Because in the second determinant we have just done following.
R2 R3 and then R1 R2 which does not change the determinant value.
In first row operation it multiplies the determinant by -1. Second row operation again multiplies it by -1. Thus it becomes equal to the first determinant.

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