Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2020MathematicsThree Dimensional Geometry

If a =2 i +3 j - k , b = i +2 j -5 k , c =3 i +5 j - k , then a vector perpendicular to a and in the plane containing b and c is

Options

  1. A17 i +21 j -123 I
  2. B-17 i +21 j -97 k
  3. C-17 i -21 j -97 k
  4. D-17 i -21 j +97 k

Correct answer

C. -17 i -21 j -97 k

Step-by-step solution

We know that, any vector perpendicular to a and in the plane containing b and c is a ( b c ) . Now, b c = | array ccc i & j & k 1 & 2 & -5 3 & 5 & -1 array |=23 i-14 j - k Again, a (b c)= | array ccc i & j & k 2 & 3 & -1 23 & -14 & -1 array | =-17 i -21 j -97 k which is reguired vector.

Practice Three Dimensional Geometry on Quantrex Academy →

More from Three Dimensional Geometry

The circum radius of the triangle formed by the points (2,-1,1),(1,-3,-5) and (3,-4,-4) is 2025Let A (2,3,5), B (-1,3,2), C ( , 5, ) be the vertices of ABC . If the median through the vertex A is equally inclined to the coordinate axes, then 2025Equation of the plane passing through the origin and perpendicular to the planes x+2 y-z=1 and 3 x-4 y+z=5 is 2025If the line joining the points i +2 j and j -2 k intersects the plane passing through the points 2 i - j , 2 j +3 k and k -2 i at r , then r ( i + j + k )= 2025The vector equation of a plane passing through the line of intersection of the planes r ( i -2 k )=3, r (2 j + k )=5 and the point i +2 j +3 k is 2025The points A (-1,2,3), B (2,-3,1), C (3,1,-2) 2025The direction cosines of the line making angles 4 , 3 and (0 < < 2 ) respectively with X , Y and Z axes are 2025If the equation of the plane passing through the point (3,2,5) and perpendicular to the planes 2 x-3 y+5 z=7 and 5 x+2 y-3 z=11 is x+b y+c z+d=0 , then 2 b+3 c+d= 2025 Full Three Dimensional Geometry list All COMEDK PYQs