Let a=i^+4j^+2k^,b=3i^−2j^+7k^and c=2i^−j^+4k^. Find a vector dwhich is perpendicular to both aand band c. d=15.
If xandy are two non-collinear vectors and ABC isa triangle with side lengths a,b,andc satisfying (20a−15b)x+(15b−12c)y+(12c−20a)(×xy)=0, then triangle ABC is a. an acute-angled triangle b. an obtuse-angled triangle c. a right-angled triangle d. an isosceles triangle
Let a,bandc be unit vectors, such that a+b+c=x,ax˙=1,bx˙=23,∣x∣=2. Then find the angel between and ×˙
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˙
For given vector, a = 2i^ j +2k^ and b = -i^ +j^ - k^ , find the unit vector in the direction of the vector a +b .
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)
In a triangle PQR,SandT are points on QRandPR, respectively, such that QS=3SRandPT=4TR˙ Let M be the point of intersection of PSandQT˙ Determine the ratio QM:MT using the vector method .