find m if the vectors [2, m, 5] and [m, -3, 7] are perpendicular.
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.
To find the value of m such that the vectors [2, m, 5] and [m, -3, 7] are perpendicular, we need to check if the dot product of the two vectors is equal to 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
In this case, we have:
[2, m, 5] * [m, -3, 7] = 2*m + m*(-3) + 5*7 = 2m - 3m + 35 = -m + 35
For the vectors to be perpendicular, the dot product should be equal to zero:
-m + 35 = 0
To solve for m, we can isolate the variable by moving 35 to the other side of the equation:
-m = -35
Dividing both sides of the equation by -1, we get:
m = 35
Therefore, the value of m that makes the vectors [2, m, 5] and [m, -3, 7] perpendicular is m = 35.