Question

Given: a + b + c = 0. Out of the three vectors a, b and
c two are equal in magnitude. The magnitude of the
third vector is
$\sqrt{2 }$
times that of either of the two having
equal magnitude. The angles between the vectors are:
(A)90°, 135°, 135°
(B) 30°, 60°, 90°
(C)45°, 45°, 90°
(D) 45°, 60°, 90°
​

Answer 1

Answer:

Explanation:The sum of vectors is zero, which 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 'p' and 'q'. Then, p = q)

Also, given that r = sqrt(2) times p

=> p^2 + q^2 = 2 * (p^2) = r^2

Hence, the triangle formed by P, Q and R obey the Pythagoras theorem. Hence, it is a right-angled triangle, with R being the hypotenuse.

So, the angle between P and Q is 90 degrees, between Q and R is 135 degrees and angle between R and P is 135 degrees.