Home
Class 12
MATHS
87.Consider the following statements in ...

87.Consider the following statements in respect of a vector `vec c=vec a+vec b,` where `|vec a|=|vec b|!=0` : 1. `vec c` is perpendicular to `(vec a-vec b)` 2. `vec c` is perpendicular to `(vec a timesvec b)`. Which of the above statements is/are correct? (a) `1` only (b) `2` only (c) Both `1` and `2` (d) Neither `1` nor `2`

Promotional Banner

Similar Questions

Explore conceptually related problems

If vec c is perpendicular to both vec a and vec b , then prove that it is perpendicular to both vec a+ vec b and vec a - vec b .

If vec c is perpendicular to both vec a\ a n d\ vec b , then prove that it is perpendicular to both vec a+ vec b\ a n d\ vec a- vec bdot

If a vector vec a is perpendicular to two non-collinear vector vec b and vec c , then vec a is perpendicular to every vector in the plane of vec b and vec c .

If vec a , vec b , vec c are mutually perpendicular unit vectors, find |2 vec a+ vec b+ vec c|dot

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

Let vec a , vec b , and vec c are vectors such that | vec a|=3,| vec b|=4 and | vec c|=5, and ( vec a+ vec b) is perpendicular to vec c ,( vec b+ vec c) is perpendicular to vec a and ( vec c+ vec a) is perpendicular to vec bdot Then find the value of | vec a+ vec b+ vec c| .

Prove that ( veca+ vec b).( vec a+ vecb)= | veca|^2+| vec b|^2 , if and only if vec a ,vec b are perpendicular, given vec a!= vec0, vec b!= vec0

( vec a+2 vec b- vec c)dot{( vec a- vec b)xx( vec a- vec b- vec c)} is equal to [ vec a\ vec b\ vec c] b. c. 2[ vec a\ vec b\ vec c] d. 3[ vec a\ vec b\ vec c]

Show that the vectors vec a-2 vec b+3 vec c , vec a-3 vec b+5 vec ca n d-2 vec a+3 vec b-4 vec c are coplanar, where vec a , vec b , vec c are non-coplanar.