Given a vector A = 3a, - 2a, - 16a, find its components normal to the plane 2x + 2y – z + 8 = 0 and tangential to it.

Q: Find a vector equation of a plane having x-intercept 4, y-intercept -1, and a z-intercept of 5.…

A: The x-intercept is 4. The y-intercept is -1. The z-intercept is 5.

Q: Write the vector equation for the line of intersection between the planes π1:x−z=−5 and π2:x−y=−1.

A:

Q: Find a vector equation with parameter t for the line through the point (7,0, –7) and parallel to the…

A: We have to find a vector equation with parameter t.

Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: Find the vector and parametric equations of the line through the points A = (2,4,7) and B =…

A:

Q: Find the equation of the plane through the point with position vector 5i-2j+3k perpendicular to the…

A:

Q: Find a unit vector parallel to the line y = 7x – 3. Use the scalar product to find the angle between…

A: The equation of given line is:.Suppose,.So,.So, the parametric equation of the line is:So, the line…

Q: Find a vector in component form that is perpendicular to the line 3x 4y = 6.

A: To find the vector in component form that is perpendicular to the given line.

Q: Find a vector equation and a parametric equation for the line that passes through the point (5, 1,…

A: We have to solve given problem:

Q: Consider the vectors: u=(-2,6), v=(-3, –4), w =i+9j, and x=8i-6j.

A:

Q: Consider the vectors a= 2i +4j-6k, b*=-31 +k and c = 3j¯- 2k. Find a un vector parallel to - 2a…

A: Given query is to find the indicated unit vector.

Q: Find the vector equation of the line passing through the point (1, 2, - 4) and x-8 y+19 z-10 x-15 у…

A: To find the equation of line perpendicular to the given lines first we find vector perpendicular to…