Home
Class 12
MATHS
Let ABCD be a parallelogram such that v...

Let ABCD be a parallelogram such that ` vec A B= vec q , vec A D= vec p""a n d""/_B A D` be an acute angle. If ` vec r` is the vector that coincides with the altitude directed from the vertex B to the side AD, then ` vec r` is given by (1) ` vec r=3 vec q-(3( vec pdot vec q))/(( vec pdot vec p)) vec p` (2) ` vec r=- vec q+(( vec pdot vec q)/( vec pdot vec p)) vec p` (3) ` vec r= vec q+(( vec pdot vec q)/( vec pdot vec p)) vec p` (4) ` vec r=-3 vec q+(3( vec pdot vec q))/(( vec pdot vec p)) vec p`

Promotional Banner

Similar Questions

Explore conceptually related problems

The vectors vec a and vec b are not perpendicular and vec c and vec d are two vectors satisfying : vec b""xxvec c""= vec b"" xxvec d"",vec a * vec d=0 . Then the vector vec d is equal to : (1) vec b-(( vec bdot vec c)/( vec adot vec d)) vec c (2) vec c+(( vec adot vec c)/( vec adot vec b)) vec b (3) vec b+(( vec bdot vec c)/( vec adot vec b)) vec c (4) vec c-(( vec adot vec c)/( vec adot vec b)) vec b

If vec a= vec p+ vec q , vec pxx vec b=0a n d vec qdot vec b=0, then prove that ( vec bxx( vec axx vec b))/( vec bdot vec b)= vec qdot

If vec a is perpendicular to vec b and vec r is non-zero vector such that p vec r+( vec rdot vec a) vec b= vec c , then vec r= vec c/p-(( vec adot vec c) vec b)/(p^2) (b) vec a/p-(( vec cdot vec b) vec a)/(p^2) vec a/p-(( vec adot vec b) vec c)/(p^2) (d) vec c/(p^2)-(( vec adot vec c) vec b)/p

The reflection of the point vec a in the plane vec rdot vec n=q is a. vec a+(( vec q- vec adot vec n))/(| vec n|) b. vec a+2((( vec q- vec adot vec n))/(| vec n|)) vec n c. vec a+(2( vec q+ vec adot vec n))/(| vec n|^2) vec n d. none of these

The projection of point P( vec p) on the plane vec rdot vec n=q is ( vec s) , then a. vec s=((q- vec pdot vec n) vec n)/(| vec n|^2) b. vec s=p+((q- vec pdot vec n) vec n)/(| vec n|^2) c. vec s=p-(( vec pdot vec n) vec n)/(| vec n|^2) d. vec s=p-((q- vec pdot vec n) vec n)/(| vec n|^2)

Line vec r= vec a+lambda vec b will not meet the plane vec rdot vec n=q , if a. vec bdot vec n=0, vec adot vec n=q b. vec bdot vec n!=0, vec adot vec n!=q c. vec bdot vec n=0, vec adot vec n!=q d. vec bdot vec n!=0, vec adot vec n=q

Prove that [ vec a , vec b , vec c+ vec d]=[ vec a , vec b , vec c]+[ vec a , vec b , vec d]

Distance of the point P( vec p) from the line vec r= vec a+lambda vec b is a. |( vec a- vec p)+((( vec p- vec a)dot vec b) vec b)/(| vec b|^2)| b. |( vec b- vec p)+((( vec p- vec a)dot vec b) vec b)/(| vec b|^2)| c. |( vec a- vec p)+((( vec p- vec b)dot vec b) vec b)/(| vec b|^2)| d. none of these

Distance of point P( vec p) from the plane vec rdot vec n=0 is a. | vec pdot vec n| b. (| vec pxx vec n|)/(| vec n|) c. (| vec pdot vec n|)/(| vec n|) d. none of these

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d). (vec b- vec c)!=0,