6. Determine a vector p with |p1=5 such that p is collinear to AB given the points A(3, -7, -1) and B(17, -12, -3).

Q: Let L be the line through the point Q = (-2, 9, -4) and direction vector -[-1, 2, -2]T. Find the two…

A: The equation of the line passing through the point x1, y1, z1 and having direction ratios l, m, n is…

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: 1. Find the vector component of the vector ū (-3, 6, 2). [28, 63, 0] in the direction of = %3D

A: We have to find vector component of u =[28, 63,0]  along the direction v=[-3, 6,2] Vector component…

Q: Consider the points P(2,4,3) and Q (1, –5,2) in 3- space. Find the position vectors rī and rz for P…

A:

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: Let L7 be the line passing through the points Q1=(3,-5, –1) and Q2=(0, 4, –10). Find a value of k so…

A: Given that L1 be the passing through the points Q1=(3,-5,-1) and Q2=(0,4,-10). And the line  L2 be…

Q: Suppose v1, v2, v3 is an orthogonal set of vectors in R°. Let w be a vector in Span(v1, v2, v3) such…

A:

Q: Use the function to find the image of v and the preimage of w. V2, V1 + V2, 2v, – v2 2 v = (5, 5), w…

A: Here we have a function,we have to find image of v and pre image of w.

Q: 3. For the vectors b= (2, -1, -2) and a = (0, 4, –3) (a) Compute the projection of vector b onto the…

A: Consider the equation

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: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

A:

Q: Consider the vectors u₁ = and the vector w = 3 H Q- W U2 = []} Uz = U2+ →→→→ →→→→ If u IS in the…

A:

Q: Find the value of k for which the vectors 4 4 -5 X = || = 4 and y = 0 1 -2 k are orthogonal.

A:

Q: Find the vector ž, which is perpendicular to vectors å = (2,3, –1) and 5 = (1,–2,3) and satisfies…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Answer is 10.1

Q: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: The velocity vector of a particle in the xy-plane is (√7, 9e³-3) for all real t. If the position of…

A: The velocity vector in the xy-plane is for all real t. If the position of theparticle at , then to…

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

A:

Q: Q1. Consider the following vectors: -- () ---- () --C) 2 3 1 3 (a) Do the vectors i, u, w span R³?…

A:

Q: 10. Let the vector v = 2i -3j + k, and the vector w = = -i+3j+ 2k. Find v x w.

A: