10. Suppose A, B, and C are vector functions whereas 1, w, and are scalar functions, which of these is correct A. VV.Vx B = v?v × B B. VA Vỹ = Vx až C. A B·Vx C = V x C • [B·A] D. A+ Vw = VA – w = 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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10. Suppose A, B, and C are vector functions whereas 2, w, and ž are scalar functions, which of these is correct?
A. VV. Vx B = v2v ×B
B. VÀ Vỹ = V × ağ
C. A B Vx C = V x C • [B· A]
D. 1+ Vo = va – w = 0
Transcribed Image Text:10. Suppose A, B, and C are vector functions whereas 2, w, and ž are scalar functions, which of these is correct? A. VV. Vx B = v2v ×B B. VÀ Vỹ = V × ağ C. A B Vx C = V x C • [B· A] D. 1+ Vo = va – w = 0
Expert Solution
Explanation:

Determine each of the given options for their correctness.

Option (A):

On the left hand side:

results in 2 and thus the dot product of ×B  and 2  results in a scalar quantity.

On the right hand side:

2 times the resultant vector of ×B is also a scalar quantity which is equal to quantity on left hand side.

Hence, option (A) is correct. 

Option (B):

On the right hand side, cross product is applied to a vector(dell operator) and a scalar quantity (λξ) which is not feasible in vectors.

Hence, option (B) is incorrect.

Option (C):

On the right hand side, cross product of a vector×C and a scalarB·A is not possible.

Hence, option C is also incorrect.

Option (D):

λ and ϖ are equal to zeros. Then,

λ+λ=λ and λ-ϖ=-ϖ

But, λ+λ=ϖ-ϖ=0 is possible only when λ=0 and ϖ=0. In other cases this is not possible.

Hence, option (D) is also incorrect.

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