Physics class 11th mcqs solution Mdcat physics mcqs solution First year physics mcqs solution Vectors mcqs solution How to find angle between two vectors
00:00Question says, the angle between the two vectors a is equal to 3i plus 4j plus 5k and b is
00:16equal to 3i plus 4j plus 5k is a, 60 degree, b, 0 degree, c, 90 degree, d, none of these. To find the angle between two vectors a and b, we will use
00:38a dot b is a dot b is equal to a b cos theta. So, a dot b is the value of a is 3i plus 4j plus 5k dot
01:07the value of b vector is 3i plus 4j plus 5k is equal to the magnitude of a is the magnitude of a is given
01:30by under root x square plus y square plus z square and the magnitude of b is also given as under root x square plus y square plus z square into cos theta.
01:48So, to simplify this, we will multiply the value of i with i, the value of j with j and the value of k with k.
02:033i dot 3i it will be 9i dot i plus 4j dot 4j it will be 16j dot j plus 5k dot 5k it will be 25k dot k is equal to
02:28under, under root, under root, under root. Now, the magnitude of a is the value of x is 3, so the square on 3 plus the value of y is 4, the square on 4 plus the value of z is 5, so the square on 5 is vector b is given as 3i plus 4j plus 5k.
02:53So, the magnitude of b will be the value of x will be the value of x is 3, so the square on 3 plus the value of y is 4, so the square on 4 plus the value of z is 5, so the square on 5, enter cos theta.
03:12cos theta. As we know that i dot i is equal to j dot j is equal to k dot k is equal to 1, so 9 into 1 it will be 9 plus 16 into 1 it will be 16 plus 25 into 1 it will be 25 is equal to
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04:0450 into under root 9 plus 16 plus 25 it will also be 50 into cos theta. So 50 will be equal
04:15to under root 50 into under root 50 it will be 50 cos theta. So we have to find angle or
04:26we can also write it as 50 cos theta is equal to 50. So cos theta will be equal to 50 divided by 50
04:39when we will take this 50 on the other side of equal it will divide. So 50 divided by 50 is equal to 1
04:48is cos theta is equal to 1. So we have to find angle. So theta will be equal to cos inverse 1
04:58is the value of cos inverse 1 is 0. So angle is obtained as 0 degree. So the correct option will be B
