lemon said:1. Determine the vector equation of the line which is parallel to the vector 2i-10j-8k and which passes through the point (5, -1, 6).
2. vector equation
3. 2i-10j-8k (5, -1, 6)
5i-j+6k+landa(2i-10j-8k)
Is this all I need to do to complete this question, please?
I don't see an equation - an equation always has = in it. Also, this Greek letter - [itex]\lambda[/itex] - is named "lambda."lemon said:Determine the vector equation
A vector equation is a mathematical representation of a line or a plane in three-dimensional space using vectors. It allows us to express the position, direction, and magnitude of a line or a plane using vector operations.
To determine if a line is parallel to another line using vector equations, we can compare the direction vectors of the two lines. If the direction vectors are scalar multiples of each other, then the lines are parallel. In this case, the line 2i-10j-8k and the line through point (5,-1,6) have the same direction vector, so they are parallel.
The vector 2i-10j-8k represents the direction of the line. The numbers (2,-10,-8) represent the coefficients of the unit vectors i, j, and k respectively, which indicate the direction and magnitude of the line in the x, y, and z directions.
To find the equation of a line using vector equations, we need to know the coordinates of a point on the line and the direction vector of the line. The equation is written as r = r0 + td, where r0 is the known point, and d is the direction vector. In this case, the equation would be r = (5,-1,6) + t(2i-10j-8k).
No, a vector equation can only represent a line in three-dimensional space. In two-dimensional space, we use parametric equations to represent a line.