Advertisements
Advertisements
प्रश्न
If the vectors `2hati-qhatj+3hatk and 4hati-5hatj+6hatk` are collinear, then value of q is
(A) 5
(B) 10
(C) 5/2
(D) 5/4
Advertisements
उत्तर
(C) 5/2
Let `bar a=2hati-qhatj+3hatk and barb=4hati-5hatj+6hatk`
Since, `bara and barb` are collinear.
∴ there exists a scalar t such that `barb = t bara `.
∴ `4hati-5hatj+6hatk=t(2hati-qhatj+3hatk)=2thati-qthatj+3thatk`
∴ By equality of vectors, we get
4 = 2t, - 5 = - qt, 6 = 3t
∵ 4 = 2t and 6 = 3t ∴t = 2
- 5 =- q(2)
–5 = – 2q
∴ 5 = 2q
q = 5/2
APPEARS IN
संबंधित प्रश्न
If the vectors `-3hati+4hatj-2hatk, hati+2hatk, hati-phatj` are coplanar, then the value of of p is
(A) -2
(B) 1
(C) -1
(D) 2
Show that the points A (-7 , 4 , -2),B (-2 , 1 , 0)and C (3 ,-2 ,2) are collinear.
If a = `3hat"i" + hat"j" - hat"k"`, b = `2hat"i" - hat"j" + 7hat"k"` and c = `7hat"i" - hat"j" + 23 hat"k"` are three vectors, then which of the following statement is true.
If the vectors `hat"i" + hat"j" + hat"k"`, `hat"i" - hat"j" + hat"k"` and `2hat"i" + 3hat"j" + "m"hat"k"` are coplanar, then m = ____________.
If p, q and r are non-zero, non-coplanar vectors then [p + q - r p - q q - r] = ______.
If `hati - 2hatj + hatk`, `2hati + phatj + 3hatk` and `5hati - 9hatj + 4hatk` are coplanar, then the value of p is equal to ______
In a trapezium, if the vector `overline(BC) = lambda overline(AD)`, `overlinep = overline(AC) + overline(BD)` is collinear with `overline(AD)` and `overlinep = mu overline(AD)`, then ______
Let `overlinea = 2hati + hatj + hatk, overlineb = hati + 2hatj - hatk` and a unit vector `overlinec` be coplanar. If `overlinec` is perpendicular to `overlinea`, then `overlinec` = ______
If the points `P(overlinea+2overlineb+overlinec)`, `Q(2overlinea+3overlineb), R(overlineb+ t overlinec)` are collinear, where `overlinea, overlineb, overlinec` are three non-coplanar vectors, the value of t is ______
If (2, 3, 9), (5, 2, 1), (1, λ, 8) and (λ, 2, 3) are coplanar, then the product of all possible values of λ is ______.
If `vecp, vecq` and `vecr` are nonzero, noncoplanar vectors then `[(vecp + vecq - vecr, vecp - vecq, vecq - vecr)]` = ______.
Let `bara = hati + 2hatj + hatk, barb = hati - hatj + hatk and barc = hati + hatj - hatk`.
A vector in the plane of `bara and barb` whose projection on `barc` is `1/sqrt3`, is
In triangle ABC, which of the following is not true?
If (2, 3, 9), (5, 2, 1), (1, λ, 8) and (A, 2, 3) are coplanar, then the product of all possible values of λ is ______.
