Home
Class 12
MATHS
The vectors x hati + (x+1)hatj + (x+2)ha...

The vectors `x hati + (x+1)hatj + (x+2)hatk, (x+3)hati+ (x+4)hatj + (x+5)hatk and (x+6)hati + (x+7)hatj+ (x+8)hatk` are coplanar if x is equal to

A

1

B

-3

C

4

D

0

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
` x hati + (x + 1) hatj + (x +2) hatk , ( x+3) hati + (x +4) hatj + ( x+5) hatk and ( x+6) hati + (x+7) hatj+ ( x+8) hatk` are coplanar. We have determinant of their coefficients
as `|{:(x,,x+1,,x+2),(x+3,,x+4,,x+5),(x+6,,x+7,,x+8):}|`
Applying `C_2 to C_2 - C_1 and C_3 to C_3-C_1`, we have
`|{:(x,,1,,2),(x+3,,1,,2),(x+6,,1,,2):}|=0`
Here , `x in R`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Reasoning Questions)|11 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Comprehension)|9 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise Exercise (Single)|34 Videos

  • INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|222 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE|Exercise All Questions|529 Videos

Similar Questions

Explore conceptually related problems

Show that the points whose position vectors are 2hati + 3hatj - 5hatk , 3hati +hatj - 2hatk and 6hati - 5hatj + 7hatk are collinear.

The value of [hati - hatj , hatj - hatk, hatk - hati] is :

Knowledge Check

  • hati *(hatj xx hatk) +hatj(hatk xx hati) +hatk (hati xx hatj) is :

    A
    -3
    B
    0
    C
    1
    D
    3

  • If vec a = hati + hatj + hatk , vecb = 2hati+xhatj+hatk, vecc = hati - hatj + 4hatk and veca. (vecbxxvecc) =0 then x is equal to

    A
    5
    B
    7
    C
    26
    D
    10

    • Similar Questions

    Explore conceptually related problems

    Show that the vectors 5hati+6hatj + 7hatk , 7hati - 8hatj + 9hatk , 3hati + 20 hatj +5hatk are coplanar.

    Find the direction cosines and direction rations for the following vectors (i) 3 hati - 4hatj + 8 hatk (ii) 3hati + hatj + hatk (iii) hatj (iv) 5 hati - 3hatj - 48 hatk (v) 3hati - 3hatk + 4 hatj (vi) hati -hatk OR ( b) Show that the points whose position vectors 4hati + 5hatj + hatk , - hatj - hatk , 3 hati + 9 hatj+ 4hatk and - 4 hati + 4 hatj + 4 hatk are conplanar.

    If the vectors (1-x) hati+hatj+hatk, hati+(I-y) hatj+hatk and hati+hatj+(1-z) hatk are coplanar vectors, then value of 1/x +1/y+1/z is (x, y, z are non zero numbers)

    Show that the points whose position vectors 4hati + 5hatj + hatk, -hatj -hatk, 3hati + 9hatj + 4hatk and -4hati + 4hatj + 4hatk are coplanar.

    Let veca =hati -hatk, vecb = xhati+ hatj + (1-x)hatk and vecc =y hati +xhatj + (1+x -y)hatk . Then veca, vecb and vecc are non-coplanar for

    The position vectors of the vertices of a triangle are hati + 2hatj + 3hatk , 3hati -4hatj + 5hatk and -2hati+ 3hatj- 7hatk . Find the perimeter of the triangle.

    Home
    Profile