Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (5,7).
If b is a vector whose initial point divides thejoin of 5i^and5j^ in the ratio k:1 and whose terminal point is the origin and ∣∣b∣∣≤37,thenk lies in the interval a. [−6,−1/6] b. (−∞,−6]∪[−1/6,∞) c. [0,6] d. none of these
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
Examine the following vector for linear independence: (1) i+j+k,2i+3j−k,−i−2j+2k (2) 3i+j−k,2i−j+7k,7i−j+13k
If a,b,andc be three non-coplanar vector and aprime,bprimeandc′ constitute the reciprocal system of vectors, then prove that r=(ra˙′)a+(rb˙′)b+(rc˙′)c r=(ra˙′)a′+(rb˙′)b′+(rc˙′)c′
Given three non-zero, non-coplanar vectors a,b,and⋅r1=pa+qb+candr2=a+pb+q⋅ If the vectors r1()+2r2and2r1+r2 are collinear, then (P,q) is a. (0,0) b. (1,−1) c. (−1,1) d. (1,1)