1& how by scalar triple product
the vol. of right triangular prism ABCA2B2C2 is 3. the position vector of the vertices of the base ABC is A=(1,0,1);B=(2,0,0)& C=(0,1,0)
Q-1)the height of the prism=
a)√3 b)√6 c)√8 d)none
Q-2) the coordinate of vertex A2 can be
a)(2,2,2) b)(0,2,0) c)(0,-2,2) d)none
Q-3) the length of the longest face diagonal will be
a)√8 b)√13 c)√11 d) none
for your convinence correct answer is: b,a,c respectively plz give solution
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7 Answers
1357first one very easy
The area of the triangle is (1/2)*√2*√3
volume=area*h=3
h=√6
1357third one
height=√6
diagonal will be longest for the longest side of triangle ABC i.e. √5
so d=√11
1how u write √2 &√3 plz explain & also explain on the basis of scalar triple product
1357by distance formula find AB, BC and AC
AB=√2
BC=√5
AC=√3
right angled triangle
1357V=(1/2)aXb.c=3
here c is the vector perpendicular to a and b
so let c=h(aXb)/|(aXb)|
where h is the height
(1/2)aXb.h(aXb)/|(aXb)|=(h/2)|(aXb)|
a=BC=-2i+j
b=CA=i-j+k
aXb=2k+2j-k+i=i+2j+k
|aXb|=√6
V=(h/2)√6=3
h=√6