ata,1,2, bl,l,0), and c (0,0,-4) 13) Find the values of x such that (3.2, v) and

Question

ata,1,2, bl,l,0), and c (0,0,-4) 13) Find the values of x such that (3.2, v) and (2x, 4,x) are orthogonal 14) Find two unit vectors that are orthogonal to both j+ 2k and i -2j+3k 15) Find the acute angle between two diagonals of a cube 16) Find a vector perpendicular to the plane through the points A(1,0,0), 8(2.0,-1) and C/1.4.3) 17) Find parametric equations for the line through (4, -1, 2) and (1, 1, 5) 18) Find parametric equations for the line through (-2, 2, 4) and perpendicular to the plane 2x-y + 5z = 12 19) Find an equation of the plane through (2, 1, 0) and parallel to x +4-3z 1 20) Find an equation of the plane through (3, -1, 1), (4, 0, 2), and (6, 3, 1) 21) Show that the planes y-z 1 and 2x -3y +4z 5 are neither parallel nor perpendicular. Find the angle between the planes.

Explanation / Answer

13. Two vectors are said to be orthogonal if their dot product is zero

so (3,2,x) and (2x,4,x) are orthogonal if

(3,2,x) . (2x,4,x) = 0

=> 6x+8+x^2=0

=> x^2+6x+8=0

=>(x+4)(x+2)=0

=> x= -4 and x= -2

only one question per post please

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.