Find a vector of magnitude 5 units, and parallel to the resultant of the vectors a=2i^+3j^−k^ and b=i^−2j^+k^.
Check whether the given three vectors are coplanar or non-coplanar. −2i^−2j^+4k^,−2i^+4j^,4i^−2j^−2k^
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
The midpoint of two opposite sides of a quadrilateral and the midpoint of the diagonals are the vertices of a parallelogram. Prove that using vectors.
′I′ is the incentre of triangle ABC whose corresponding sides are a,b,c, rspectively. aIA+bIB+cIC is always equal to a. 0 b. (a+b+c)BC c. (a+b+c)AC d. (a+b+c)AB
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′
If the resultant of three forces F1=pi^+3j^−k^,F2=6i^−k^andF3=−5i^+j^+2k^ acting on a parricle has magnitude equal to 5 units, then the value of p is a. −6 b. −4 c. 2 d. 4