00:00Question says, the angle between two vectors minus 2i plus 3j plus k and i plus 2j minus
00:164k is a 0 degree, b 90 degree, c 180 degree, d none of these.
00:28Suppose the first one is vector a and second one is vector b. Vector a is minus 2i plus
00:443j plus k and vector b is given as i plus 2j minus 4k. So, we have to find angle between
01:03these two vectors. So, to find the angle between these vectors, we will use the formula is
01:10a dot b is equal to ab cos theta or after rearranging this equation, this equation will be cos theta
01:29will be equal to a dot b upon ab. So, cos theta will be equal to a dot b. The value of a is
01:46i plus 2i plus 3j plus k dot the value of b is i plus 2j minus 4k divided by the magnitude
02:08of a. The magnitude of a is calculated by the formula under root x square plus y square plus
02:15z square. So, here the value of x is minus 2, the value of y is 3, the value of z is 1. So,
02:27minus 2 square plus 3 square plus 1 square. And the magnitude of b, the value of b along x axis is 1,
02:48along y axis is 2 and along z axis is minus 4. So, the square of 1, the square of 2 and the square of minus 4
03:05because the value of z is minus 4k. So, cos theta will be equal to, for simplification, we will multiply
03:16the value of i with i, the value of j with j and the value of k with k. So, minus 2i dot i plus 3 to the 6
03:34plus j dot j plus into minus minus 4k dot k divided by the square of minus 2 is plus 4, the square of 3 is 9,
03:51the square of 1 is 1, the square of 1 is 1, the square of 2 is 4, the square of minus 4 is plus 16.
04:03So, cos theta will be equal to, as we know that i dot i is equal to j dot j is equal to k dot k is equal to 1.
04:20So, this will become minus 2 plus 6 minus 4 because the value of i dot i is 1, the value of j dot j is also 1, the value of k dot k is also 1.
04:38So, 4 plus 9, it will be 13 plus 1, under root 14, enter 4 plus 16, 20 plus 1, it will be under root 21.
05:00So, plus 6 minus 2 minus 4, it will be minus 6 divided by under root 14 into under root 21.
05:19So, 0 divided by something, it will be 0. So, cos theta will be equal to 0 or theta will be equal to cos inverse 0 because we have to find angle is
05:26the value of cos inverse 0 is the value of cos inverse 0 is 90 degree.
05:33So, angle is obtained is 90 degree. So, angle is obtained is 90 degree. So, the correct option will be
05:40B 90 degree.
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