Question

If a,b,c,d are 4 vectors find angle between ab and cd

Answer 1

Given, C=A×B and D= B×A. What is the angle between C and D?

Answer

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4 ANSWERS



Rishabh Sharma, Student at Pranveer Singh Institute of Technology, Kanpur (2016-present)

Answered Jun 27, 2017

Here we have to apply the concept of vectors .

First you have to know that C,A,B,D all are vectors.

And the cross product of two vectors is also a vector having direction perpendicular to the plane having the two parent vectors .

And you should also know about the properties of vectors .

If there are two vectors having same magnitude and same direction thn they are considered to be equa. Means if vector Z and Y are having same direction and magnitude then Z=Y.But if there are two vectors having same magnitude but opposite in direction they are known as opposite vectors. Means if Z and Y Are having same magnitude but opposite in direction then Z= -Y here the negative sign before vectors Y shows its opposite direction .Now the third property. If Z×Y= X and if Y×Z =W then X = -W . Means (Z×Y = -Y×Z) here again the negative sign before Y×Z shows its opposite direction with respect to Z×Y.

Now here C represents A×B and here A×B Is the cross product therefore the vector C will be perpendicular to the plane containing vectors A and B.

Now as D represents the cross product of vectors B and A and here D is the resultant therefore it also have its direction perpendicular to the plane containing B and A

Now applying property discussed above

(A×B)= -(B×A) and as A×B = C and B×A = D

therefore

C = - D

Now again apply the property discussd above.

Means here the vector C and D are in opposite direction means the angle between them is 180° .

Thanks for reading.

SHAKUNTALAM GHOSH.