00:00Question is, the angle between the two vectors a is equal to 5i plus 5j and b is equal to
00:155i minus 5j will be a 0 degree, b 45 degree, c 90 degree, d 180 degree.
00:28First, we have to find angle between two vectors a and b, so to find the angle between two vectors
00:38we will use the formula as a dot b is equal to a b cos theta, as the value of a is given
00:54is 5i plus 5j, the value of a is 5i plus 5j dot the value of b is obtained as 5i minus 5j is equal to
01:15the magnitude of a, the magnitude of a is calculated by using formula under root x square plus y square
01:23plus z square, here the value of x and y is given, so the value of x is 5, so the square and 5 and the
01:33root the magnitude of b, here in b the value of x and y is given, so the value of x is 5, so the square
01:50on 5 plus the value of y is minus 5, so the square on minus 5 into cos theta. So for simplification, we will
02:01multiply the value of i with i and the value of j with j, so 5 5 the 25 i dot i plus into minus, it will be minus 5 5 the 25 j dot j is equal to
02:2317. Under root
02:25under root
02:26under root, the square of 5 is 25 plus 25 under root 25 unda root 25 plus 25, the square of minus 5 is also plus 25
02:36into cos theta
02:42So, as i.i is equal to 1 and j.j is also equal to 1, so 25 minus 25 will be equal
02:58to under root 25 plus 25 it will be 50 into under root 50 cos theta. So, plus 25
03:10will be get cancelled with minus 25, so it will be 0 is equal to under root 50
03:16into under root 50 it will be 50 cos theta. As we have to find angle, so by
03:23rearranging this equation we can also write this as 50 cos theta is equal to
03:310, cos theta will be equal to here 50 is multiplying on the other side of equal
03:39it will divide with 0, so 0 divided by something will be equal to 0. We have
03:45to find angle, so theta will be equal to cos inverse 0 as the value of cos inverse
03:530 is 90 degree, so angle is obtained as 90 degree. So, the correct option will be C
04:0690 degree.
04:13you
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