106Q1. volume of parallelopiped = [a b c] = √[a b c][a b c]
now use [a b c][u v w]
= l a.u a.v a.w l
l b.u b.v b.w l
l c.u c.v c.w l
The answer ull get is 1/√2
1.the edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors a cap , b cap, c cap. such that dotproduct of any of these unit vectors taken 2 at a time is 1/2. Find volume of parallelopiped.
2.let two non collinear vectors a cap and b cap form a an acute angle. A point P moves in such a way that at any time t the pos vector OP(O is origin) is given by
a cap cos t + bcap sin t. When P is farthest from origin O, let M be the length of OP vector and ucap be the unit vector along OP. Find ucap and M
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4 Answers
106
1357alternative way
a+b, c, axb are in the same plane
let the angle between c and a+b is A
a+b has magnitude of √3
c.(a+b)/√3=cosA
cosA=1/√3
sinA=√(2/3)
angle between c and axb is 90-A
V=c.(axb)=cos(90-A)sin60=sinAsin60=√(2/3)*√3/2=1/√2