2.6. Find the distance from a vector (1, 2, 3, 4) to the subspace spanned by the vectors v₁ = (1,-1, 1, 0)² and v₂ = (1,2,1,1) (note that v₁v₂). Can you find the distance without actually computing the projection? That would simplify the calculations.

Q: 13. Find a vector equation of the line through (2, 1) parallel to (x, y) = (-2,7)+t(3,5). 14. Find a…

A:

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

Q: Q5) the value of the constant a for which the line x=2+t,y=2+3t,z=3+t and the plane ax+y-2z-7=0 are…

A: We will use definition.

Q: Find a vector v parallel to the intersection of the planes - (x + y + 3z) = 4 and 3y - 3x - z = 7.…

A: Step 1: Step 2: Step 3: Step 4:

Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

A:

Q: use the vectors u = , v = , and w = a) Find which pair(s) of vectors from that set is/are…

A: We have to check

Q: How did you get the vectors and to get a cross product for a perpendicular vector to i+j and j+k.

A: How did you get the vectors <1,1,0> and <0,1,1> to get a cross product for a…

Q: ? (2,3), (0,0) }

A: Let S=2, 3, 0, 0. We need to find whether the set S spans a line or all of ℝ2.

Q: Find a linear map T that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

A:

Q: Find a linear map 7 that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

A:

Q: Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A:

Q: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

A:

Q: Find the equation of the plane P spanned by vectors  v = (2,1, 3)  and w = (1,2,-1)  containing the…

A: The given problem is to find the equation of plane P that is spanned by given two vectors and…

Q: Suppose the straight lines L₁ and L2 have respective vector equations 5 4 r1 = -3 + t 3 where s and…

A:

Q: a. A nonzero vector perpendicular to both [-1. 3, 4] and [-2. -1, 3].  b. The distance from (2, -1,…

A: Let's go through each of the questions:a. To find a nonzero vector perpendicular to both [−1,3,4]…

Q: 6. Project the vector b = (1, 4, 2) onto the plane S that contains the vectors a₁ = (1, 2, 1) and a2…

A: