Find the values of x such that the vectors u^vector = and v^vector = are orthogo

Question

Find the values of x such that the vectors u^vector = and v^vector = are orthogonal. x = -2, x= 2 x = -1, x = 2 x = -2, x = 4 x = -3, x = -1 x = -1, x = 3 Let a^vector = and b^vector = . Find a vector that is perpendicular to both a^vector and b^vector. Find the vector projection, proj_a^vector b^vector, of b^vector on a^vector, where a^vector = i + 2 j - 4k, b^vector = 5 i- j + k -1/Squareroot 21 1/27 1/21 1/21 -1/21 Find an equation of the line that passes through the point (-1, 1, 4) and is perpendicular to the plane x + 2y + 3z = 4.

Explanation / Answer

Question 5) If u and v are orthogonal, then u.v =0

=> x.x + (-2).x + 3.(-1) = 0

=> x2 -2x -3 =0

=> (x+1)(x-3)=0

=> x=-1 , x=3

Option e) is correct

Question 6) Here in option e) ; <-1,-1,2>.a = <-1,-1,2>.<1,0,1/2> = -1+0+1 = 0

Also <-1,-1,2>.b = <-1,-1,2>.1,2,3/2> = -1-2+3 = -3+3 = 0

Hence option e) is correct that is <-1,-1,2> is perpendicular to both a and b

Question 7) Vector projectiob of b on a is given by :

projab = a.b/|a|2 .a

a.b = (i + 2j -4k).(5i -j +k) = 5-2-4 = 5-6 = -1

|a|2 = (i + 2j - 4k).(i + 2j - 4k) = 1+4+16 = 21

projab = a.b/|a|2 .a = -1/21 (i+2j-4k) = -1/21 <1,2,-4>

Option e) is correct

Question 8) The line passing through (-1,1,4) is given by (-1,1,4)+t(x1, y1, z1)

The direction vector is <1,2,3>

Hence equation of line is (-1,1,4) + t(1,2,3) = <-1+t, 1+2t, 4+3t>

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

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