If in parallelogram ABCD, diagonal vectors are AC=2i^+3j^+4k^ and BD=−6i^+7j^−2k^, then find the adjacent side vectors AB and AD
Prove, by vector method or otherwise, that the point of intersection of the diagonals of a trapezium lies on the line passing through the midpoint of the parallel sides (you may assume that the trapezium is not a parallelogram).
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 the projections of vector a on x -, y - and z -axes are 2, 1 and 2 units ,respectively, find the angle at which vector a is inclined to the z -axis.
Find the vector of magnitude 3, bisecting the angle between the vectors a=2i^+j^−k^ and b=i^−2j^+k^˙
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.
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