Find the area of a triangle having the pointsA(1,1,1), B(1,2,3)and C(2,3,1)as its vertices.
If the resultant of three forces F1=pi^+3j^−k^,F2=6i^−k^andF3=−5i^+j^+2k^ acting on a parricle has magnitude equal to 5 units, then the value of p is a. −6 b. −4 c. 2 d. 4
Find the value of λ so that the points P,Q,R and S on the sides OA,OB,OC and AB, respectively, of a regular tetrahedron OABC are coplanar. It is given that OAOP=31,OBOQ=21,OCOR=31 and ABOS=λ˙ (A) λ=21 (B) λ=−1 (C) λ=0 (D) for no value of λ
The points with position vectors 60i+3j,40i−8j,ai−52j are collinear if a. a=−40 b. a=40 c. a=20 d. none of these
Column I, Column II Collinear vectors, p.a Coinitial vectors, q. b Equal vectors, r. c Unlike vectors (same intitial point), s. d
A isa vector with direction cosines cosα,cosβandcosγ˙ Assuming the y−z plane as a mirror, the directin cosines of the reflected image of A in the plane are a. cosα,cosβ,cosγ b. cosα,−cosβ,cosγ c. −cosα,cosβ,cosγ d. −cosα,−cosβ,−cosγ
Given three points are A(−3,−2,0),B(3,−3,1)andC(5,0,2)˙ Then find a vector having the same direction as that of AB and magnitude equal to ∣∣AC∣∣˙