Two vectors are perpendicular if their dot product is zero.
The dot product of two vectors [a, b, c] and [d, e, f] is given by the formula: a*d + b*e + c*f.
So, we need to find the dot product of vectors [2, m, 5] and [m, -3, 7] and set it equal to zero.
(2 * m) + (m * -3) + (5 * 7) = 0
2m - 3m + 35 = 0
-m + 35 = 0
To solve for m, we can subtract 35 from both sides:
-m = -35
Finally, we can multiply both sides by -1 to solve for m:
m = 35
Therefore, if m = 35, the vectors [2, m, 5] and [m, -3, 7] are perpendicular.
find m if the vectors [2, m, 5] and [m, -3, 7] are perpendicular.
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