The vector product of a and b is -23 i + 7 j + 6 k
Step-by-step explanation:
If a = 2i + 4j + 3k and b = i + 5j - 2k
We need to find the vector product of a and b
1. Put the two vectors in the form of matrix 3 by 3, the 1st row is i , j , k
the second row is vector a and the 3rd row is vector b
2. Find its determinant in terms of i , j , k
3. The dot product of the resultant vector and each vector must be 0
[tex]\left[\begin{array}{ccc}i&j&k\\2&4&3\\1&5&-2\end{array}\right][/tex]
a × b = i[(4)(-2) - (3)(5)] - j[(2)(-2) - (3)(1)] + k[(2)(5) - (4)(1)]
a × b = i[(-8) - 15] - j[(-4) - 3] + k[10 - 4]
a × b = -23 i + 7 j + 6 k
This should be perpendicular to both a and b, hence the dot product
should be zero
∵ a = 2i + 4j + 3k
∴ [a × b] . a = (-23)(2) + (7)(4) + (6)(3) = -46 + 28 + 18 = 0
∵ b = i + 5j - 2k
∴ [a × b] . b = (-23)(1) + (7)(5) + (6)(-2) = -23 + 35 - 12 = 0
The vector product of a and b is -23 i + 7 j + 6 k
Learn more:
You can learn more about vectors in brainly.com/question/1592430
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