Question

При каком значении n векторы а(3;-5;n) и b(n;1;2)-перпендикулярны?

Answer 1

Векторы перпендикулярны  тогда, когда их скалярное произведение равно нулю:

Answer 2

Perpendicularity of Vectors

When are the vectors a(3;-5;n) and b(n;1;2) perpendicular?

Two vectors are perpendicular if their dot product is zero. In this case, the dot product of the two vectors a and b should be zero for them to be perpendicular.

The dot product of two vectors a and b is given by the formula: a · b = a1b1 + a2b2 + a3b3.

So, for the vectors a and b to be perpendicular, their dot product should be zero: 3n + (-5) * 1 + n * 2 = 0.

Therefore, the vectors a and b are perpendicular when 3n - 5 + 2n = 0.

This simplifies to 5n - 5 = 0.

Solving for n, we get n = 1.

So, the vectors a(3;-5;1) and b(1;1;2) are perpendicular when n = 1.