The vector a=(sinθ,-2) is known to be perpendicular to the vector b=(1, cosθ), where θ belongs to (0,π/2). 2 If 5 cos (θ-φ)=3 times 5 cosφ.0 The vector a=(sinθ,-2) and vector b=(1, cosθ) are known to be perpendicular to each other, where θ belongs to (0,π/2). 2 If 5 cos (θ-φ)=3 times 5 cosφ.0

The vector a=(sinθ,-2) is known to be perpendicular to the vector b=(1, cosθ), where θ belongs to (0,π/2). 2 If 5 cos (θ-φ)=3 times 5 cosφ.0 The vector a=(sinθ,-2) and vector b=(1, cosθ) are known to be perpendicular to each other, where θ belongs to (0,π/2). 2 If 5 cos (θ-φ)=3 times 5 cosφ.0

(1) Vector vertical, sinθ-2cosθ=0 and sin2θ+cos2θ=1
θ Belongs to (0,π/2) cos 2θ=1/5
Cosθ=√5/5, sinθ=2√5/5
(2)5 Cos (θ-φ)=3√5 cosφ
5(Cos θ cos sin θ sinφ)=3√5 cosφ
√5 Cos 2√5sinφ=3√5 cosφ
Sinφ= cosφ
Sinφ= cosφ=√2/2

Can a zero vector become a direction vector? Would you please be more thorough... Could a zero vector become a direction vector? Everyone, please speak clearly...

Not allowed
His direction is arbitrary.
And
The purpose of a direction vector is to indicate a direction

No. No.
His direction is arbitrary.
And
The purpose of a direction vector is to indicate a direction

If the non-zero vectors a and b are in the same or opposite direction, then the direction of a+b must be the same as the direction of one of a and b. If a and b are mutually opposite vectors, add up to 0 vectors, then is the direction of the zero vector the same as the direction of vector a?

No. No.
(1) When the directions of the non-zero vectors A and B are the same, the direction of the vector A+vector B is the same as the direction of the vectors A and B
(2) When the directions of the non-zero vectors A and B are opposite and the moduli of the vectors A and B are not equal, the direction of the vector A+vector B is the same as the direction of the vector whose moduli are large.
When the directions of the non-zero vectors A and B are opposite and the moduli of the vectors A and B are equal, the vector A+vector B is with arbitrary directions.
The direction of the zero vector is arbitrary and is not necessarily the same as the direction of the vector a

The product of two vectors is -1 What is the relationship between these two vectors?

These two vectors are opposite

Given A (2,1,0), point B is in plane xOz, if the direction vector of line AB is (3,-1,2), then the coordinate of point B is

Let B be (a,0, b), then AB=(a-2,-1, b)=(3,-1,2),
A-2=3, b=2
Solve a=5, b=2, so
Point B coordinates are (5,0,2)

Let A, B, C, D be four points in the plane, and let A (1,3), B (2,-2), C (4,1)1, if vector AB=CD, find the coordinate of D point 2, let a=vector AB, b=BC, find the projection of vector a in direction b Let A, B, C, D be four points in the plane, and let A (1,3), B (2,-2), C (4,1)1, if the vector AB=CD, find the coordinate of D point 2, let a=vector AB, b=BC, find the projection of vector a in direction b

Let the coordinates of point D be D (x, y), vector AB=(2,-2)-(1,3)=(1,-5), vector CD=(xy)-(4,1)=(x-4, y-1). vector AB=vector CD, x-4=1, x=5; y-1=-5, y=-4.1. The coordinates of point D is D (5,-4).2. Vector AB=a, vector a=(1,-5)|a|=√26; vector BC=b, vector b=(2,3),|...