Show that the vectors 2i^−j^+k^,i^−3j^−5k^and 3i^−4j^−4k^form the vertices of a right angled triangle.
If xandy are two non-collinear vectors and a, b, and c represent the sides of a ABC satisfying (a−b)x+(b−c)y+(c−a)(×xy)=0, then ABC is (where ×xy is perpendicular to the plane of xandy ) a. an acute-angled triangle b. an obtuse-angled triangle c. a right-angled triangle d. a scalene triangle
In a quadrilateral PQRS,PQ=a,QR,b,SP=a−b,M is the midpoint of QRandX is a point on SM such that SX=54SM˙ Prove that P,XandR are collinear.
The points with position vectors 60i+3j,40i−8j,ai−52j are collinear if a. a=−40 b. a=40 c. a=20 d. none of these
The vectors xi^+(x+1)j^+(x+2)k^,(x+3)i^+(x+4)j^+(x+5)k^and(x+6)i^+(x+7)j^+(x+8)k^ are coplanar if x is equal to a. 1 b. −3 c. 4 d. 0
Statement 1:Let A(a),B(b)andC(c) be three points such that a=2i^+k^,b=3i^−j^+3k^andc=−i^+7j^−5k^˙ Then OABC is a tetrahedron. Statement 2: Let A(a),B(b)andC(c) be three points such that vectors a,bandc are non-coplanar. Then OABC is a tetrahedron where O is the origin.
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)