Show that the points A, B and C with position vectors, a=3i^−4j^−4k^, b=2i^−j^+k^and c=i^−3j^−5k^ respectively form the vertices of a right angled triangle.
ABCD parallelogram, and A1andB1 are the midpoints of sides BCandCD, respectivley . If ∀1+AB1=λAC,thenλ is equal to a. 21 b. 1 c. 23 d. 2 e. 32
Two forces AB and AD are acting at vertex A of a quadrilateral ABCD and two forces CB and CD at C prove that their resultant is given by 4EF , where E and F are the midpoints of AC and BD, respectively.
If A(−4,0,3)andB(14,2,−5), then which one of the following points lie on the bisector of the angle between OAandOB(O is the origin of reference )? a. (2,2,4) b. (2,11,5) c. (−3,−3,−6) d. (1,1,2)
If a,b,candd are four vectors in three-dimensional space with the same initial point and such that 3a−2b+c−2d=0 , show that terminals A,B,CandD of these vectors are coplanar. Find the point at which ACandBD meet. Find the ratio in which P divides ACandBD˙
Find a vector magnitude 5 units, and parallel to the resultant of the vectors a=2i^+3j^−k^ and b=i^−2j^+k^˙
A man travelling towards east at 8km/h finds that the wind seems to blow directly from the north On doubling the speed, he finds that it appears to come from the north-east. Find the velocity of the wind.
If a,b,andc are mutually perpendicular vectors and a=α(a×b)+β(b×c)+γ(c×a)and[abc]=1, then find the value of α+β+γ˙