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Given that vector A+b+c=0.out of three vectors two are equal in magnitude and the magnitude of the third vector is root two times that of either of the two having equal magnitude.then the angles between vectors

Given that vector A+b+c=0.out of three vectors two are equal in magnitude and the magnitude of the third vector is root two times that of either of the two having equal magnitude.then the angles between vectors

Grade:12th

2 Answers

Arun
25763 Points
3 years ago
Given that the sum of vectors is zero implies that these vectors form a triangle.
Also, two vectors are equal in magnitude. So, the triangle formed by these vectors is an isosceles triangle. (Let the equal sides of triangle be 'a' and 'b' without loss of generality. Then, a = b)
Also, given that c = sqrt(2) times a
=> a^2 + b^2 = 2 * (a^2) = c^2
Hence, the triangle formed by A, B and C obey the pythagoras theorem. Hence, it is a right angled triangle, with C being the hypotenuse.

So, the angle between A and B is 90 degrees, between B and C is 135 degrees and angle between C and A is 135 degrees.
Ajeet Tiwari
askIITians Faculty 86 Points
one year ago
hello students

From polygon law, three vectors having summation zero should form, a closed polygon(triangle). Since, the two vectors are having same magnitude and the third vector is2times that of either of two having equal magnitude, i.e., the triangle should be right angled triangle.
Angle between A and B,α=90o
Angle between B and C,β=135o
Angle between A and C,γ=135o.

hope it helps
Thankyou and Regards

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