The scalar product of the vector i^+j^+k^with a unit vector along the sum of vector 2i^+4j^−5k^and λi^+2j^+3k^is equal to one. Find the value of λ.
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∣∣˙
A man travelling towards east at 8km/h finds that the wind seems to blow directly from the north On doubling the speed, he finds that it appears to come from the north-east. Find the velocity of the wind.
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)
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.
A unit vector of modulus 2 is equally inclined to x - and y -axes at an angle π/3 . Find the length of projection of the vector on the z -axis.
A vector has components p and 1 with respect to a rectangular Cartesian system. The axes are rotted through an angel αabout the origin the anticlockwise sense. Statement 1: IF the vector has component p+2and 1 with respect to the new system, then p=−1. Statement 2: Magnitude of the original vector and new vector remains the same.