For any two vectors →aand →bwe always have ∣→a→˙b∣≤∣→a∣∣→b∣(Cauchy-Schwartz inequality).
If a,bandc are three non-zero vectors, no two of which ar collinear, a+2b is collinear with c and b+3c is collinear with a, then find the value of ∣∣a+2b+6c∣∣˙
If vectors a=i^+2j^−k^,b=2i^−j^+k^andc=lambdai^+j^+2k^ are coplanar, then find the value of (λ−4)˙
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˙
OABCDE is a regular hexagon of side 2 units in the XY-plane in the first quadrant. O being the origin and OA taken along the x-axis. A point P is taken on a line parallel to the z-axis through the centre of the hexagon at a distance of 3 unit from O in the positive Z direction. Then find vector AP.
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˙
The position vector of the points PandQ are 5i^+7j^−2k^ and −3i^+3j^+6k^ , respectively. Vector A=3i^−j^+k^ passes through point P and vector B=−3i^+2j^+4k^ passes through point Q . A third vector 2i^+7j^−5k^ intersects vectors AandB˙ Find the position vectors of points of intersection.