00:00Question says, the angle between the vectors i plus j and j plus k is a 30 degree, b 45
00:16degree, c 60 degree, d 90 degree. Suppose the vector a is given as i plus j and vector b is given as j plus k.
00:40So, we have to find angle between these two vectors. To find the angle, we will use the formula as a dot b is equal to ab cos theta.
00:57So, the value of a is i plus j dot the value of b is j plus k is equal to the magnitude of a. The magnitude of a is calculated by using formula under root x square plus y square plus z square.
01:20Here, the value of x and y is given because we will use i along x-axis and j along y-axis. So, the value of x is 1, so the square on 1 and the value of y is also 1 the square on 1.
01:40So, first we will take i and multiply with this square on 1, so the value of z is also 1, so the square on 1 plus the value of z is also 1, so the square on 1.
02:05So, first we will take i and multiply with this bracket, so i dot j plus k. Now, we will take j and we will multiply with this bracket dot j plus k is equal to the square of
02:33square of 1 is 1 and also the square of 1 is 1 into under root 1 plus 1 cos theta so i dot j
02:46plus i dot k plus j dot j plus j dot k is equal to under root 2 under root 2 into cos theta as we know
03:09that i dot j is equal to i dot k is equal to j dot k is equal to 0 means the dot product between two
03:23different unit vectors will be 0 but j dot j will be equal to 1 so this will become 0 plus 0 plus 1
03:38plus 0 is equal to under root 2 into under root 2 it will be 2 cos theta so 1 is equal to 2 cos theta
03:52we have to find the angle or we can also write this as 2 cos theta is equal to 1 so cos theta is equal to
04:051 here 2 is multiplying on the other side of equal it will divide so we have to find angle so theta
04:22will be equal to cos theta will be equal to cos inverse 1 upon 2 as the value of cos inverse 1 upon 2 is 60 degree
04:34so the correct option will be c 60 degree means angle between i plus j and j plus k is obtained as 60 degree
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