Find the vector joining the points P(2,3,0)and Q(1,2,4)directed from P to Q.
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
Statement 1: The direction cosines of one of the angular bisectors of two intersecting line having direction cosines as l1,m1,n1andl2,m2,n2 are proportional to l1+l2,m1+m2,n1+n2˙ Statement 2: The angle between the two intersection lines having direction cosines as l1,m1,n1andl2,m2,n2 is given by cosθ=l1l2+m1m2+n1n2˙
If the resultant of two forces is equal in magnitude to one of the components and perpendicular to it direction, find the other components using the vector method.
ABCD is a tetrahedron and O is any point. If the lines joining O to the vrticfes meet the opposite faces at P,Q,RandS, prove that APOP+BQOQ+CROR+DSOS=1.
The position vectors of the points PandQ with respect to the origin O are a=i^+3j^−2k^ and b=3i^−j^−2k^, respectively. If M is a point on PQ, such that OM is the bisector of ∠POQ, then OM is a. 2(i^−j^+k^) b. 2i^+j^−2k^ c. 2(−i^+j^−k^) d. 2(i^+j^+k^)
If AO+OB=BO+OC , then A,BnadC are (where O is the origin) a. coplanar b. collinear c. non-collinear d. none of these