Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5).
If r1,r2,r3 are the position vectors of the collinear points and scalar pandq exist such that r3=pr1+qr2, then show that p+q=1.
Let a,b,andcanda′,b′,c′ are reciprocal system of vectors, then prove that a′×b′+b′×c′+c′×a′=[abc]a+b+c .
Find the least positive integral value of x for which the angel between vectors a=xi^−3j^−k^ and b=2xi^+xj^−k^ is acute.
If a=7i^−4k^andb=−2i^−j^+2k^, determine vector c along the internal bisector of the angle between of the angle between vectors aandbsuchthat∣c∣ =56
Given three points are A(−3,−2,0),B(3,−3,1)andC(5,0,2)˙ Then find a vector having the same direction as that of AB and magnitude equal to ∣∣AC∣∣˙
Statement 1: The direction cosines of one of the angular bisectors of two intersecting line having direction cosines as l1,m1,n1andl2,m2,n2 are proportional to l1+l2,m1+m2,n1+n2˙ Statement 2: The angle between the two intersection lines having direction cosines as l1,m1,n1andl2,m2,n2 is given by cosθ=l1l2+m1m2+n1n2˙