00:00The question is, if a is equal to 3i plus j plus 2k and b is equal to 2i minus 2j plus
00:154k, then the value of mod of a cross b will be, means the value of the magnitude of cross
00:27product will be a, 8 under root 2, b, 8 under root 3, c, 8 under root 5, d, 5 under root
00:398.
00:41So first of all, we will find the cross product a cross b, which is equal to, we will find
00:58the cross product by using determinant form.
01:04So first of all, we will write i, j and k.
01:12The value of a is, along i is 3, along j is 1 and along k is 2.
01:25The value of b, along i is 2, along j is minus 2 and along k is 4.
01:37So a cross b will be obtained as, first of all, we will take i.
01:48So this column will be neglected.
01:53So 1 into 4, it will be 4, minus, minus 2 into 2, it will be minus 4.
02:05So minus j, so this column will be neglected.
02:11So we will multiply 3, 2 with 2, 4.
02:20So 3 for the 12, minus 2 to the 4.
02:27Now we will take plus k.
02:32So the column of k will be neglected.
02:38So 3 into minus 2, it will be minus 6, this minus is a formula.
02:48So 2 into 1, it will be 2.
02:52So a cross b will be equal to i into 4, minus into minus, it will be plus 4, minus j into
03:0712, 12 minus 4, it will be 8, plus k into minus 6, minus 2, it will be minus 8.
03:23So a cross b will be obtained as 4 plus 4, it will be 8 into i, it will be 8i, minus into plus,
03:37it will be minus 8j, plus into minus, it will be minus 8k.
03:45Now we will find the magnitude of a cross b will be equal to under root x square plus y square plus z square or z square.
04:04So by putting the given values, the value of x is 8, so the square on it plus the value of y is minus 8, so the square on minus 8, so the square on minus 8, so the square on minus 8, so the magnitude of a cross b will be equal to
04:32the square of minus 8, so the square of minus 8 is also plus 64, the square of minus 8 is also plus 64, so 64 plus 64 plus 64, it will be 192.
04:54So we can also write this is 64, so the magnitude of a cross b will be obtained as the under root of 64 is 8, so it will be 8 under root 3.
05:24So the correct option will be b, 8 under root of 64.
05:26So the correct option will be b, 8 under root of 64.
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