Question

4. IfĀ .B. = A x B . Then angles between Ā and Bºis:
a. 30°
b. 45°
C. 60°
d. 90°​

Answer 1

$\huge \mathfrak{solution}$

Given:

A•B=A×B

As we know that ,

A•B= ABCOS@ [ dot product]

And

A×B= ABSIN@ [Cross product]

Put the values,

=> ABCOS@=ABSIN@

=>COS@=SIN@

=>SIN@/COS@=1

=>TAN@=1

=>TAN@=TAN45°

=>@=45°

Hence the angle between A and B is

45°

Answer 2

Answer:

Given:

Dot product of 2 vectors is equal to the cross product of the same 2 vectors.

To find:

Angles between the vectors

Calculation:

As per the question, the vectors are A and B

Dot product = Cross product

=> | A . B | = | A × B |

=> A × B × cos(θ) = A × B × sin(θ)

=> tan(θ) = 1

=> θ = 45°

So, angle between the vectors is 45°

Things to note:

• I have used magnitude sign because, cross product itself gives another vector.
• The question requires the magnitude of cross product and not it's direction.
• Dot product is already a Scalar Quantity, hence use of magnitude sign is not mandatory.