00:00Question says, the angle between the two vectors a is equal to 3i plus 4j plus 5k and b is
00:14equal to 3i plus 4j minus 5k will be a 90 degree, b 0 degree, c 60 degree, d 45 degree.
00:26To find the angle between two vectors a and b, we will use a dot b is equal to a b cos theta or this formula will become as cos theta is equal to a dot b upon a b.
00:53Because here a b is multiplying with cos theta on the other side of equal it will divide, so this will become as.
01:03So cos theta will be equal to a dot b is the value of a is 3i plus 4j plus 5k dot the value of b is 3i plus 4j minus 5k.
01:19The value of b is 3i plus 4j minus 5k divided by the magnitude of a is magnitude is calculated by using formula under x square plus y square plus z square.
01:31So the magnitude of a 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 value of z is 5.
01:49So the square on 5. So the square on 5 into the magnitude of b. The b vector is given as 3i plus 4j minus 5k. So the value of x is 3. So 3 square plus 3i plus 4j minus 5k.
02:11So the value of x is 3. So 3 square plus the value of y is 4. So the square on 4. The value of z is minus 5. So the square on minus 5.
02:29So cos theta will be equal to 5. So cos theta will be equal to. 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.
02:44So 3i dot 3i. So 3i dot 3i. It will be 9i dot i plus 4j dot 4j. It will be 16j dot j. Plus into minus. It will be minus 5k dot 5k. It will be 25k dot k.
03:10Divided by under root. The square of 3 is 9. The square of 4 is 16. The square of 5 is 25.
03:24And to under root. The square of 3 is 9. The square of 4 is 16. The square of minus 5 is plus 25k.
03:36as we know that i.i is equal to j.j is equal to k.k is equal to 1, means i.i is also equal to 1,
03:51j.j is equal to 1 and k.k is also equal to 1. So, cos theta will be equal to 9 plus 16 minus 25,
04:05divided by 9 plus 16 plus 25, it will be under root 50 into 9 plus 16 plus 25, it will be under root 50.
04:219 plus 16, it will be 25 minus 25 divided by under root 50 into under root 50, it will be 50.
04:35So, plus 25 will be get cancelled with minus 25. So, it will be 0 upon 50 is we have to find angle. So,
04:50theta will be equal to cos inverse is 0 upon 50 will be equal to 0. So, cos inverse 0 is the value of cos
05:03inverse 0 is 90 degree. So, angle is obtained is 90 degree. So, the correct option will be a 90 degree.
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