00:00Question is, what is the unit vector perpendicular to the following vectors 2i plus 2j minus
00:12k and 6i minus 3j plus 2k?
00:18a i plus 10j minus 18k divided by 5 into under root 17.
00:26d i minus 10j plus 18k divided by 5 into under root 17.
00:33c i minus 10j minus 18k divided by 5 into under root 17.
00:42d i plus 10j plus 18k divided by 5 into under root 17.
00:53So, the first one is the value of a and the second one is the value of b.
01:01is the value of a is given as 2i plus 2j minus k and the value of b vector is given as 6i minus 3j plus 2k.
01:28So, we have to find the unit vector perpendicular to these vectors.
01:35to these vectors is c vector is equal to the a cross b so unit vector perpendicular will be equal to a cross b.
01:53So, unit vector perpendicular will be equal to a cross b divided by means vector divided by its magnitude.
02:00So, first of all we will find the vector then its magnitude so first of all we will find the vector then its magnitude.
02:07So, first of all we will find the vector then its magnitude so first of all we will find a cross b.
02:14a cross b a cross b will be equal to a cross b will be equal to we will use determinant form i, j and k.
02:21the value of a along x axis is 2.
02:28along y axis is also 2 and along z axis is minus 1.
02:35means the value of a along i is 2 along j is plus 2 and along k is minus 1.
02:42the value of b along i is 6 along j is 6 along j is 6 along j is minus 3 and along k is 6.
02:49the value of b along j is minus 3 and along k is plus 2.
02:56so, first of all we will take i along y axis is 2 along y axis is also 2 and along z axis is minus 1.
02:59means the value of a along i is 2 along j is plus 2 and along k is minus 2.
03:04the value of b along i is 6 along j is minus 3 and along k is plus 2.
03:14so, first of all we will take i as we will neglect the column of i so we will multiply 2 with 2 and minus 3 with minus 1 so 2 to the 4 minus.
03:31minus 3 into minus 1 it will be plus 3 because minus into minus it will be plus.
03:39then we will take i as we will neglect the column of i so 2 to the 4 minus 6 into minus 1 it will be minus 6.
04:01now we will take plus k so this column will be neglected so 2 3 d minus 6 minus 2 6 d 12 so a cross b will be equal to
04:30equal to plus 4 minus 3 it will be 1 so 1 into i it will be plus i minus j 4 minus into minus it will be plus 6 plus k minus 6 minus 12 it will be minus 18.
04:57so a cross b so a cross b so a cross b will be equal to i 4 plus 6 10.
05:076, 10. So, minus into plus it will be minus, so minus 10j, plus into minus it
05:17will be minus 18k. So, A cross B is obtained as I minus 10j minus 18k. Now we
05:28will find the unit vectors, is unit vectors is equal to the vectors divided
05:39by its magnitude. So, vector A cross B is obtained as I minus 10j minus 18k divided
05:55by its magnitude is, magnitude is calculated by using formula under root x
06:03square plus y square plus z square. So, the value of x is 1, the square on 1 plus y
06:11square, the value of y is minus 10. So, the square on minus 10 plus the value of z
06:18is minus 18. So, the square on minus 18. So, I minus 10j minus 18k divided by the
06:35square of 1 is 1, the square of minus 10 is 100, the square of minus 18 is 324,
06:47so, the unit vectors perpendicular to the vectors A and B is equal to I minus 10j minus 18k divided by
07:05under root 100 plus 324, it will be 424, it will be 425, or we can also write this as I minus 10j minus 18k divided by
07:31under root 25 into 17. So, this will be equal to I minus 10j minus 18k divided by the under root of 25 is 5
07:52under root 17. So, the correct option will be C I minus 10j minus 18k divided by 5 under root 17.
08:13So, the sole i minus 10j minus 10k divided by the outer root 17 because the value of x is 424, it will be 6,'ll be ahem.
08:18And then, simply file, which reminds me of 299, this don't have slight
08:22addition to the value of x is 5. So, the value of x is 5, 6,일� mile, which means 19 timesє to conquer multiple
08:24types of x, orc if plus 10 , the mass e is 10% loan, which means 20. So, it will be a detailed
08:27لا quality of x is 18 and equal to remember 325, so 1. So, the 안녕하세요, the permeability of x is 20. So, the responses 3 times is 15,
08:30there will be a handful of x will� at h. So, 1. So, measure half a dimension
Comments