A(6,3,3), B(3,5,1) and C(-1,3,5)are the point in a three-dimensional space. Find, a) The vector BA and BC in terms of i, j,k. Hence, show that BA is perpendicular to BC. b) A unit vector that is perpendicular to plane containing the point A, B and C. c) A Cartesian equation of the plane described in (b).

Q: Give the parametric and symmetric equations of the line that passes through the point (4, -3,5) and…

A: Using the dot product equal to zero for perpendicular to the vectors.

Q: b) Find parametric and vector equations for the line through (2,3,0) perpendicular to the vectors u…

A:

Q: Given points A(1,2,3), B(0,-3,-2) and C(-1,0,5): a) Determine vector, parametric and symmetric…

A: Given

Q: Determine a vector equation for each line. a) perpendicular to line 4x - 3y = 17 and through point…

A:

Q: 3. A plane contains A(1, -3, 2), B(-2, 4, 2) and C(3, 2, 1). (a) Determine the vector equation of…

A:

Q: Consider the points A(-3,-3,-1), B(-1,–5,-4), C(-5, -6, -3). - a) Find the unit vector in the…

A:

Q: t a = (3,3) and b = (4,1) draw and label the vectors a, b, -a and b - a on a set of coordinate axes.

A: Given vectors a=(3, 4) and b=(4, 1)

Q: The vertices of a triangle in space are (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3). Explain how to…

A: Given:

Q: nd he position vector in the form of xr+ yr for the vector that starts at the point (-1, 2), ends at…

A: Given query is to find the vector ,it's magnitude and direction.

Q: Give the parametric and symmetric equations of the line that passes through the point (5,−1,3) and…

A:

Q: Find a) vector A and magnitude of A, b) the angle between A and the y-axis, c) vector B.

A: According to Bartleby expert guidelines, I have solved only first 3 subparts of the given question.…

Q: Let vector a=4i-5j+3k and a point P(2,-1,3). If the length of PQ is equal to the length of vector a,…

A: We need to choose correct option. NOTE - As per our guidelines we can solve one question