If i^+j^+k^,2i^+5j^,3i^+2j^−3k^and i^−6j^−k^are the position vectors of points A, B, C and D respectively, then find the angle between ABand CD. Deduce that ABand CD
In a four-dimensional space where unit vectors along the axes are i^,j^,k^andl^,anda1,a2,a3,a4 are four non-zero vectors such that no vector can be expressed as a linear combination of others and (λ−1)(a1−a2)+μ(a2+a3)+γ(a3+a4−2a2)+a3+δa4=0, then a. λ=1 b. μ=−2/3 c. γ=2/3 d. δ=1/3
Two forces AB and AD are acting at vertex A of a quadrilateral ABCD and two forces CB and CD at C prove that their resultant is given by 4EF , where E and F are the midpoints of AC and BD, respectively.
Statement 1: If cosα,cosβ,andcosγ are the direction cosines of any line segment, then cos2α+cos2β+cos2γ=1. Statement 2: If cosα,cosβ,andcosγ are the direction cosines of any line segment, then cos2α+cos2β+cos2γ=1.
If vectors a=i^+2j^−k^,b=2i^−j^+k^andc=lambdai^+j^+2k^ are coplanar, then find the value of (λ−4)˙
A,B,CandD have position vectors a,b,candd, respectively, such that a−b=2(d−c)˙ Then a. ABandCD bisect each other b. BDandAC bisect each other c. ABandCD trisect each other d. BDandAC trisect each other
If AndB are two vectors and k any scalar quantity greater than zero, then prove that ∣∣A+B∣∣2≤(1+k)∣∣A∣∣2+(1+k1)∣∣B∣∣2˙
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