Home
Class 11
MATHS
Vector 1/3 (2hati - 2hatj +hatk) is...

Vector `1/3 (2hati - 2hatj +hatk) ` is

A

a unit vector

B

makes an angle `pi//3` with vector `(2hati- 4hatj + 3hatk) `

C

parallel to vector `( -hati + hatj - 1/2 hatk)`

D

perpendicular to vector `3hati + 2hatj - 2hatk`

Text Solution

Verified by Experts

The correct Answer is:
a,c,d
`veca=1/3(2hati-2hatj+hatk)`
`|veca|^(2)=1/9(4+4+1)=1or |veca|=1`
Let `vecb = 2hati - 4hatj + 3hatj`, then
` cos theta = (veca.vecb)/(|veca||vecb|) = 5/sqrt29 Rightarrow vecc ||veca`
Let `vecd = 3hati + 2hatj + 2hatk, " then " veca. vecd =0 Rightarrrow veca bot vecd`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise JEE Previous Year (Single Question)|28 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|1316 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE|Exercise Solved Examples And Exercises|320 Videos

Similar Questions

Explore conceptually related problems

The unit vector which is orthogonal to the vector 5hati + 2hatj + 6hatk and is coplanar with vectors 2hati + hatj + hatk and hati - hatj + hatk is

A vector coplanar with vectores hati + hatj and hatj + hatk and parallel to the vector 2 hati - 2 hatj - 4 hatk is

Find a unit vector parallel to the sum of the vector (hati + hatj + hatk) and (2hati - 3hatj + 5hatk) .

The unit vector which is orthogonal to the vector 5hatj + 2hatj + 6hatk and is coplanar with vectors 2hati + hatj + hatk and hati - hatj + hatk is

If the projection of the vector hati + 2 hatj + hatk on the sum of the two vectors 2hati + 4hatj - 5hatk and -lamdahati+2hatj+ 3hatk is 1, then lamda is equal to _______

Unit vectors equally inclined to the vectors hati , 1/3 ( -2hati +hatj +2hatk) = +- 4/sqrt3 ( 4hatj +3hatk) are

Find a unit vector in the diection of the vector. (i) (3hati + 4hatj - 5hatk) , (ii) (3hati - 2hatj + 6hatk) (iii) (hati + hatk) , (iv) (2hati + hatj + 2hatk)

The componant of vector 2 hati -3 hatj +2hatk perpendicular to the vector hati + -3 hatj + hatk is-

Determine the sine of the angle between the vectors 3 hati +hatj +2hatk and 2hati - 2hatj +4hatk .