Question

Given the following expression
A) \((\overset{⃗}{a}\times \overset{⃗}{b})\cdot \overset{⃗}{c}\)
B) \(\overset{⃗}{a}\times (\overset{⃗}{b}\cdot \overset{⃗}{c})\)
C) \(\overset{⃗}{a}\cdot (\overset{⃗}{b}\cdot \overset{⃗}{c})\)
D) \(|\overset{⃗}{a}|(\overset{⃗}{b}\cdot \overset{⃗}{c})\)
E) \((\overset{⃗}{a}\cdot \overset{⃗}{b})\times (\overset{⃗}{b}\cdot \overset{⃗}{c})\)
Then which of the following is not correct

• A. B and E are meaningful
• B. A and D are meaningful
• C. B, C and E are meaningless
• D. A is meaningful but B is meaningless

Hint:

A cross product needs two vectors and a dot product gives a scalar; check that each operation is defined.

Answer 1

The Correct Option is A

Step 1: Approach
Classify each piece as vector or scalar, then judge the operation.

Step 2: Classification
A: vector-dot-vector gives scalar, defined. B: vector times scalar through a cross, undefined. C: vector dot scalar, undefined. D: scalar times scalar, defined. E: scalar cross scalar, undefined.

Step 3: Judge the options
Option (B) says A and D are meaningful, true. Option (C) says B, C, E are meaningless, true. Option (D) says A is meaningful but B is meaningless, true. Option (A) says B and E are meaningful, false.

Step 4: Answer
The incorrect statement is (A).

Final Answer:
Expressions B and E are meaningless, so the claim that they are meaningful is the incorrect one, option (A). \[ \boxed{\text{(A)}} \]