Home
Class 12
MATHS
Given the vectors vec A , vec B ,a n d ...

Given the vectors ` vec A , vec B ,a n d vec C` form a triangle such that ` vec A= vec B+ vec Cdot` find `a ,b ,c ,a n dd` such that the area of the triangle is 56 where ` vec A=a hat i+b hat j+c hat k` ` vec B=d hat i+3 hat j+4 hat k` ` vec C=3 hat i+ hat j-2 hat k`

Text Solution

Verified by Experts

The correct Answer is:
a= -8, b=4, c=2, d =-11
Here, `vecA,vecB and vecC` are the vectors representing the sides of triangle ABC, where `vecA= ahati + bhatj +chatk`
`vecB = hati + 3hatj + 4hatk and vecC = 3hati + hatj - 2hatk`
Given that `vecA =vecB +vecC`, Therefore,
`ahati + bhatj + chatk = (d+3) hati + 4hatj + 2hatk`
` Rightarrow a=d +3, b=4,c=2`
`vecB xxvecC= |{:(hati ,hatj ,hatk),(d,3,4),(3,1,-2):}|`
`10 hati + (2d + 12) hatj + (d -9) hatk`
Area of `triangle = 1/2 |vecB xx vecC|`
`1/2 sqrt([100 + (2d + 12)^(2) + (d-9)^(2)])`
`5 sqrt6`
` or sqrt((5d^(2)+30d + 325)) = 10 sqrt6`
`or 5d^(2) + 30d - 275 = 0 or d^(2) + 6 d - 55 =0`
`or (d +11) (d-5) =0
`Rightarrow d=5 or -11 `
where d= 5 a= 8, b= 4 and c=2 and where d = -11 , a = -8 ,b =4 and c= 2
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercises MCQ|134 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Reasoning type|8 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.3|18 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

Similar Questions

Explore conceptually related problems

Given the vectors vec A , vec B ,a n d vec C form a triangle such that vec A= vec B+ vec Cdot find a ,b ,c ,a n dd such that the area of the triangle is 5sqrt6 where vec A=a hat i+b hat j+c hat k vec B=d hat i+3 hat j+4 hat k vec C=3 hat i+ hat j-2 hat k

if vec a= 5 hat i -hat j -3 hat k and vec b=hat i+3 hat j - 5 hat k , Find vec a . vec b =?

If vec a= 2 hat i- hat j+ hat k and vec b = - hat i+3 hat j+4 hat k ,then veca.vecb =

Find vec adot vec b when: vec a= hat j- hat k\ a n d\ vec b=2 hat i+3 hat j-2 hat k

Find | vec axx vec b| , if vec a= hat i-7 hat j+7 hat k and vec b=3 hat i-2 hat j+2 hat kdot

if vec a = 2 hat i- 3 hat j+hat k and vec b = hat i+2 hat j- 3hat k then vec aXvec b is

Find vec axx vec b ,\ if\ vec a=2 hat i+ hat k\ a n d\ vec b= hat i+ hat j+ hat kdot

Find the angle between the vectors vec a= hat i+hat j-hat k and vec b=hat i-hat j+hat k

Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i+ hat j- hat kdot Then find [vec a vec b vec c]

Find the area of triangle (i) drawn on the vectors vec(a) = 6 hat (i) + 2 hat (j) - 3 hat (k) and vec (b) = 4 hat (i) - hat (j) - 2 hat (k)