The dot products of vector with the vectors (i+j-3k), (i+3j-2k) and (2i+j+4k) are 0,5,8 respectively. Find the vector.
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Let unkown vector be a = xi + yj + zk
b = i+j-3k
c=i+3j-2k
d=2i +j+4k
A/Q a.b = x + y -3z = 0
a.c = x + 3y -2z = 5
a.d = 2x+y+4z = 8
Now we can solve these 3 linear equations using determinant.
gives x = 41/13 y = -14/13 z = 9/13
Hence vector a = 41/13 i - 14/13 j + 9/13 k
Hope my answer is correct.
b = i+j-3k
c=i+3j-2k
d=2i +j+4k
A/Q a.b = x + y -3z = 0
a.c = x + 3y -2z = 5
a.d = 2x+y+4z = 8
Now we can solve these 3 linear equations using determinant.
gives x = 41/13 y = -14/13 z = 9/13
Hence vector a = 41/13 i - 14/13 j + 9/13 k
Hope my answer is correct.
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