00:03Question 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. Suppose the first one is
00:31vector a and second
00:32one is vector b. Vector a is minus 2i plus 3j plus k and vector b is given as i
00:53plus 2j minus 4k.
01:00So, we have to find angle between these two vectors. So, to find the angle between these vectors,
01:09we will use the formula is a dot b is equal to a b cos theta or after rearranging this
01:24equation,
01:25this equation will be cos theta will be equal to a dot b upon a b. So, cos theta will
01:42be equal to a dot b.
01:44The value of a is minus 2i plus 3j plus k dot the value of b is i plus 2j
02:01minus 4k divided by
02:07the magnitude of a. The magnitude of a is calculated by this formula under root x square plus y square
02:16plus z square. So, here the value of x is minus 2, the value of y is 3, the value
02:25of z is 1.
02:26So, minus 2 square plus 3 square plus 1 square. And the magnitude of b, the value of b along
02:45x axis is 1,
02:48along y axis is 2, and along z axis is minus 4. So, the square of 1, the square of
02:582, 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
03:17the value of i with i, the value of j with j, and the value of k with k. So,
03:25minus 2i dot i,
03:32plus 3 to the 6j dot j, plus into minus minus 4k dot k, divided by, the square of minus
03:482 is plus 4,
03:49the square of 3 is 9, the square of 1 is 1, the square of 1 is 1, the square
03:57of 2 is 4, the square of minus 4
04:01is plus 16. So, cos theta will be equal to, as we know that, i dot i is equal to
04:15j dot j is equal to,
04:17so, k dot k is equal to 1. So, this will become is minus 2 plus 6 minus 4, because
04:30the value of i dot i is 1,
04:33the value of j dot j is also 1, the value of k dot k is also 1.
04:444 plus 9, it will be 13 plus 1, under root 14, enter, 4 plus 16, 20 plus 1, it
04:58will be under root 21.
05:02So, plus 6 minus 2 minus 4, it will be minus 6, divided by, under root 14 into under root
05:1821.
05:29So, 0 divided by something, it will be 0. So, cos theta will be equal to 0, or theta will
05:42be equal to cos inverse 0,
05:46because we have to find angle, is the value of cos inverse 0 is 90 degree. So, angle is obtained
05:56is 90 degree.
06:00So, the correct option will be B 90 degree.
06:06So, the value of C 30 degree.
06:06So, let , point tommy.
06:07You know, while the J is a 70 degree.
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