Question

При яких значеннях a вектори c(2;-3;8) d(-7;-2;a ) перпендикулярні?​

Answer 1

2*(-7)+(-3)*а+8*(-2)=0

-14-3а-16=0

-3а=30

а=-10

Answer 2

Perpendicular Vectors

To determine when the vectors c(2, -3, 8) and d(-7, -2, a) are perpendicular, we can use the dot product. Two vectors are perpendicular if and only if their dot product is zero.

The dot product of two vectors c and d is calculated by multiplying the corresponding components of the vectors and summing the results:

c · d = c1 * d1 + c2 * d2 + c3 * d3

In this case, we have:

c(2, -3, 8) · d(-7, -2, a) = 2 * -7 + (-3) * (-2) + 8 * a

To find the values of a for which the vectors are perpendicular, we need to solve the equation:

2 * -7 + (-3) * (-2) + 8 * a = 0

Simplifying the equation, we get:

-14 + 6 + 8a = 0

-8 + 8a = 0

8a = 8

a = 1

Therefore, the vectors c(2, -3, 8) and d(-7, -2, 1) are perpendicular when a = 1.