The angle between the vectors a=3i-4j, and b=4i+3j,?

a) 0degrees b)90degrees c)180degrees d)45degrees

The angle between the vectors a=3i-4j, and b=4i+3j,?
a . b = |a| |b| cos θ


(12 - 12) = (5) (5) cos θ


cos θ = 0


θ = 90°


OPTION b)
Reply:Thank you for your vote. Report It

Reply:It's 90 degrees, because a dot b = 0.


In general a dot b = |a| |b| cos t,


where t is the angle between the vectors.
Reply:the dot product of the two vectors is 0.





thus the two vectors are perpendicular.





the angle between them is 90°





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Reply:Given:


a=3i-4j


b=4i+3j





Here ,


a1 = 3 a2= -4


b1=4 b2= 3





Formula:





Angle between two vectors, THETA: cos-1{ [(a1*b1) + (a2*b2)]/(|a|*|b|) }





|a| = SQRT [ a1^2 + a2^2 ]


= SQRT [ 3^2 + (-4)^2 ]


=SQRT [ 9+16 ]


=SQRT (25)


|a| = 5





Similiarly,





|b| = SQRT [ b1^2 +ba2^2 ]


= SQRT [ 4^2 + 3)^2 ]


=SQRT [ 16+9 ]


=SQRT (25)


|b| = 5





Therefore, Theta = cos-1{ [(3*4) + (-4*3)]/(5*5) }


= cos-1{ [(3*4) + (-4*3)]/(5*5) }


= cos-1{ [12-12] / 25 }


= cos-1{ 0 }


Theta = 90 degrees
Reply:a.b=3.4-4.3


=12-12


=0


so Cos( x)=0


=Cos90degrees


so x=90degrees


hence 'b' is the right answer.
Reply:90 degrees
Reply:Both vectors can be described by:


a = (3, -4)


b = (4, 3)





The dot product of two vectors equals the product of the vectors lengths times the cos of the angle between them. Or:





a (dot) b = |a||b|cos(theta)





a (dot) b


= (3, -4) (dot) (4, 3)


= (3*4) + (-4*3)


= (12) + (-12)


= 0





The only way for |a||b|cos(theta) to equal zero is if cos(theta) is equal to zero.





cos(theta) = 0


theta = cos^-1(0)


theta = 90 degrees

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