VectorHard
Question
If 
and 
are linearly dependent vectors and 
, then
and are linearly dependent vectors and , thenOptions
A.α = 1, β = - 1
B.α = 1, β = 
1
1C.α = - 1, β = 1
1D.α = 1, β = 1
1, β = 1Solution
Since, 
are linearly dependent vectors.
⇒
⇒
= 0
Applying C2 → C2 - C1, C3 → C3 - C
⇒
= 0
⇒ -(β - 1) = 0 ⇒ β = 1
Also,
(given)
⇒ 1 + α2 + β2 = 3 (given
)
⇒ 1 + α2 + 1 = 3
⇒ α2 = 1 ⇒ α =1
are linearly dependent vectors.⇒
⇒
= 0 Applying C2 → C2 - C1, C3 → C3 - C
⇒
= 0⇒ -(β - 1) = 0 ⇒ β = 1
Also,
(given) ⇒ 1 + α2 + β2 = 3 (given
)⇒ 1 + α2 + 1 = 3
⇒ α2 = 1 ⇒ α =
1Create a free account to view solution
View Solution FreeMore Vector Questions
Vector has components A1, A2, A3 along the three axes. If the co-ordinates system is rotated by 90o about z-axis, then t...If î + ĵ + , 2î + 5ĵ, 3î + 2ĵ − 3 and î − 6ĵ − be p.v. of four...If = 4î − 2ĵ + 3 and = 4î − 8ĵ − 6 are two vectors then , are-...For any vector , the value of is equal to...Let P(3, 2, 6) be a point in space and Q be a point on the line . Then the value of μ for which the vector is paral...