Home
Class 12
MATHS
Find a unit vector perpendicular to th...

Find a unit vector perpendicular to the plane determined by the points `(1,-1,2),(2,0,-1) and (0,2,1)dot`

Text Solution

Verified by Experts

Given points are A(1,-1,2),B(2,0,-1) and C(0,2,1)
`Rightarrow vec(AB)=veca=hati+hatj-3hatk,vec(BC)=vecb=-2hati+2hatj+2hatk`
`vecaxxvecb=|{:(hati,hatj,hatk),(1,1,-3),(-2,2,2):}|=8hati+4hatj+4hatk`
Hence, Unit vector `vecaxxvecb=|{:(hati,hatj,hatk),(1,1,-3),(-2,2,2):}|=8hati+4hatj+4hatk`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.1|18 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.2|15 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

Similar Questions

Explore conceptually related problems

The unit vector perendicular to the plane determined by P (1,-1,2) ,C(3,-1,2) is ________.

Find the equation of the plane passing through the points (2,1,0),(5,0,1) and (4,1,1) .

In each of the following find a unit a vector perpendicular to both vec (a) and vec (b) vec(a) = (2,1,1) and vec(b) = (1,-1,2)

Find the equation of the plane passing through the point(1,2,1) and perpendicular to the line joining the points (2,3,5) and (1,4,2).

Find the equation of the plane passing through the point (1,2,1) and perpendicular to the line joining the points (1,4,2) and (2,3,5). Also find the coordinates of the foot of the perpendicular and the perpendicular distance of the point (4,0,3) from the above found plane.

Find the equation of the plane which passes through the points (1,2,3),(2,3,1) and (3,1,2)

Find the equation of the plane which passes through the points (1,2,3) ,(2,3,1) and (3,1,2).

Find the distance between the point (1+sqrt2,1-sqrt2) and (0,0)

Find the equation of the plane passing through the points (2,1,0),(5,0,1) and (4,1,1) If P is the point (2,1,6) then find point Q such that PQ is perpendicular to the above plane and the mid point of PQ lies on it.

By vector method find the area of the triangle whose vertices are (1,1,1) ,(2,0,1) and (3,-2,0)