Vector =kb vector
Kb vector =(kx, k) (constant multiplied by vector equals every term of vector multiplied by this constant)
So kx=4 and k=-2. (Two vectors are equal to each other)
So x=-2
2. Solution: Tell you an ingenious method. Take the midpoint o (0,0) of ab as the center and R=2 as the radius.
Make a circle. Obviously, this circle passes through A and B, which is ab, which is the diameter of the circle.
If the straight line is separated from the circle, there is no point P that makes pa perpendicular to pb.
When the tangent is the tangent point p, the connecting lines pa and pb are just diameters, and the corresponding circumferential angles are right angles.
Only one point P makes pa perpendicular to pb.
If they intersect, the two intersections are right angles. There are two points.
There is only one point except that the straight line passes through A or B (because A or B itself is P at this time, it cannot be a straight line).
After the above analysis
Only consider the case that it is tangent to the circle and passes through a or b.
When tangent, the distance from the O center to the straight line is radius =2.
That is, the absolute value under the radical sign (3 * 0-4 * 0+m)/(3 2+4 2 = 2.
m=+/- 10。
When a intersects with a, substitute a into a straight line.
3 *(2)-0+m = 0，m=6
When a straight line passes through b, substitute b into the straight line.
3*2-0+m=0，m=-6
Comprehensive appeal statement m=+/- 10, m=+/-6.
This is the idea of combining numbers with shapes. The analysis is to make you understand that specific questions can be omitted.
Ha ha! I wonder if the handwriting is clear.