यदि a=b+c, तब क्या यह सत्य है कि | ∣a∣=∣∣b∣∣+∣c∣ ? अपने उत्तर की पुष्टि कीजिए।
If D,EandF are three points on the sides BC,CAandAB, respectively, of a triangle ABC such that the CDBD,AECE,BFAF=−1
Points A(a),B(b),C(c)andD(d) are relates as xa+yb+zc+wd=0 and x+y+z+w=0,wherex,y,z,andw are scalars (sum of any two of x,y,znadw is not zero). Prove that if A,B,CandD are concylic, then ∣xy∣∣∣a−b∣∣2=∣wz∣∣∣c−d∣∣2˙
If i^−3j^+5k^ bisects the angle between a^and−i^+2j^+2k^,wherea^ is a unit vector, then a. a^=1051(41i^+88j^−40k^) b. a^=1051(41i^+88j^+40k^) c. a^=1051(−41i^+88j^−40k^) d. a^=1051(41i^−88j^−40k^)
A ship is sailing towards the north at a speed of 1.25 m/s. The current is taking it towards the east at the rate of 1 m/s and a sailor is climbing a vertical pole on the ship at the rate of 0.5 m/s. Find the velocity of the sailor in space.
Vectors a=i^+2j^+3k^,b=2i^−j^+k^ and c=3i^+j^+4k^, are so placed that the end point of one vector is the starting point of the next vector. Then the vector are (A) not coplanar (B) coplanar but cannot form a triangle (C) coplanar and form a triangle (D) coplanar and can form a right angled triangle