00:00Question is angle between the vectors i plus j and j minus k is a 90 degree, b 0 degree,
00:14c 180 degree, d 60 degree. Suppose vector a is given as i plus j and vector b is given as j minus k.
00:31So, we have to find the angle between these two vectors. So, to find the angle, we will use the
00:39formula. a dot b is equal to ab cos theta is the value of a is i plus j dot the value of b is j minus k
00:59is equal to the magnitude of a. So, under root is the value of x is 1. So, the square
01:09on 1 plus the value of y is also 1. So, the square on 1 because magnitude is calculated
01:19by using formula under root x square plus y square plus z square and the magnitude of b
01:28is here the value of y and z is given. The value of y is 1 plus the value of z is minus 1. So, the square
01:39on minus 1 into cos theta. So, first we will multiply i with this bracket and then we will multiply j with this
01:51bracket. So, i dot j minus k plus j dot j minus k is equal to the square of 1 is 1 into
02:10cos theta. So, i dot j minus i dot k plus j dot j plus into minus it will be minus j dot k is equal to under root 2 into under root 2 into cos theta.
02:17as we know that i dot j is equal to 0 and also plus 1 into cos theta. So, i dot j minus i dot k plus j dot j plus into minus it will be minus j dot k is equal to under root 2 into under root 2 into cos theta.
02:42So, as we know that i dot j is equal to 0 and j dot k is also equal to 0 but i dot i is equal to 1, j dot j is equal to 1 and k dot k is also equal to 1.
03:06because the same dot problems because the same dot product of unit vector is always 1, above y dot j is equal to 1 because the same dot product of unit vectors is always 0.
03:13is 0. So, this will become 0 minus 0 because i dot k is also equal to 0 plus 1 minus 0
03:34is equal to under root 2 into under root 2 it will be 2 cos theta. So, 1 is equal to 2 cos theta
03:44or we can also write this equation as 2 cos theta is equal to 1 as we have to find angle.
03:54So, cos theta is equal to 1 upon 2 because here 2 is multiplying on the other side of equal
04:05it will divide with 1. So, we have to find theta. So, theta will be equal to cos inverse
04:131 upon 2 as the value of cos inverse 1 upon 2 is 60 degree. So, angle is obtained as 60
04:24degree. So, the correct option will be d 60 degree.
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