Show that the points A(1, 2, 7), B(2, 6, 3) and C(3,10,1)are collinear.
Statement 1: If uandv are unit vectors inclined at an angle αandx is a unit vector bisecting the angle between them, then x=(u+v)/(2sin(α/2)˙ Statement 2: If DeltaABC is an isosceles triangle with AB=AC=1, then the vector representing the bisector of angel A is given by AD=(AB+AC)/2.
Statement 1: a=3i+pj+3k and b=2i+3j+qk are parallel vectors if p=9/2andq=2. Statement 2: if a=a1i+a2j+a3kandb=b1i+b2j+b3k are parallel, then b1a1=b2a2=b3a3˙
In a trapezium, vector BC=αAD˙ We will then find that p=AC+BD is collinear withAD˙ If p=μAD, then which of the following is true? a. μ=α+2 b. μ+α=2 c. α=μ+1 d. μ=α+1
i. Prove that the points a−2b+3c,2a+3b−4cand−7b+10c are are collinear, where a,b,c are non-coplanar. ii. Prove that the points A(1,2,3),B(3,4,7),andC(−3,−2,−5) are collinear. find the ratio in which point C divides AB.
Let A(t)=f1(t)i^+f2(t)j^andB(t)=g(t)i^+g2(t)j^,t∈[0,1],f1,f2,g1g2 are continuous functions. If A(t)andB(t) are non-zero vectors for all tandA(0)=2i^+3j^,A(1)=6i^+2j^,B(0)=3i^+2i^andB(1)=2j^+6j^ Then,show that A(t)andB(t) are parallel for some t.
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