find m if the vectors [2, m, 5] and [m, -3, 7] are perpendicular.

Answer 1

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.