Let us define the length of a vector ai^+bj^+ck^as∣a∣+∣b∣+∣c∣˙ This definition coincides with the usual definition of length of a vector ai^+bj^+ck^ is and only if a. a=b=c=0 b. any two of a,b,andc are zero c. any one of a,b,andc is zero d. a+b+c=0
Let ABC be triangle, the position vecrtors of whose vertices are respectively i^+2j^+4k^ , -2i^+2j^+k^and2i^+4j^−3k^ . Then DeltaABC is a. isosceles b. equilateral c. right angled d. none of these
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
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
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′
Statement 1: If ∣∣a+b∣∣=∣∣a−b∣∣, then a and b are perpendicular to each other. Statement 2: If the diagonal of a parallelogram are equal magnitude, then the parallelogram is a rectangle.