If θ is the angle between two vectors aand b, then a⋅b≥0only when
(A) 0<θ<2π (B) 0≤θ≤2π (C) 0<θ<π (D) 0
A uni-modular tangent vector on the curve x=t2+2,y=4t−5,z=2t2−6t=2 is a. 31(2i^+2j^+k^) b. 31(i^−j^−k^) c. 61(2i^+j^+k^) d. 32(i^+j^+k^)
If vectors a=i^+2j^−k^,b=2i^−j^+k^andc=lambdai^+j^+2k^ are coplanar, then find the value of (λ−4)˙
Let ABC be triangle, the position vecrtors of whose vertices are respectively i^+2j^+4k^ , -2i^+2j^+k^and2i^+4j^−3k^ . Then DeltaABC is a. isosceles b. equilateral c. right angled d. none of these
Let A(t)=f1(t)i^+f2(t)j^andB(t)=g(t)i^+g2(t)j^,t∈[0,1],f1,f2,g1g2 are continuous functions. If A(t)andB(t) are non-zero vectors for all tandA(0)=2i^+3j^,A(1)=6i^+2j^,B(0)=3i^+2i^andB(1)=2j^+6j^ Then,show that A(t)andB(t) are parallel for some t.
Three coinitial vectors of magnitudes a, 2a and 3a meet at a point and their directions are along the diagonals if three adjacent faces if a cube. Determined their resultant R. Also prove that the sum of the three vectors determinate by the diagonals of three adjacent faces of a cube passing through the same corner, the vectors being directed from the corner, is twice the vector determined by the diagonal of the cube.
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
If 4i^+7j^+8k^,2i^+3j^+24and2i^+5j^+7k^ are the position vectors of the vertices A,BandC, respectively, of triangle ABC , then the position vecrtor of the point where the bisector of angle A meets BC is a. 32(−6i^−8j^−k^) b. 32(6i^+8j^+6k^) c. 31(6i^+13j^+18k^) d. 31(5j^+12k^)