CUET Preparation Today
CUET
-- Mathematics - Section B1
Vectors
A vector →a=(x,y,z) makes an obtuse angle with Y-axis, and make equal angles with →b=(y,−2z,3x) and →c=(2z,3x,−y) and →a is perpendicular to →d=(1,−1,2) if |→a|=2√3 then vector →a is: |
(1, 2, 3) (2, –2, –2) (–1, 2, 4) None of these |
(2, –2, –2) |
→a.→b|→b|=→a.→c|→c|⇒xy−2zy+3xz√y2+4z2+9z2=2xz+3xy−yz√4z2+9x2+y2 ⇒ 2xy - yz - zx = 0 …… (i) →a.→d ⇒ x - y + z = 0 …… (ii) Putting x = y - 2z in (i) 2(y - 2z)y + yz - (y - 2z)z = 0 ⇒2y2+4zy+2z2=0⇒y2+z2−2zy=0⇒(z−y)2=0⇒z=y So, x = -z →a≡(x,−x,−x)&√3x2=2√3⇒3x2=12⇒x2=4⇒x±2 →a≡(2,−2,−2) [obtuse angle with y-axis] |