Home
Class 12
MATHS
Statement 1: vecA=2hati + 3hatj + 6hatk ...

Statement 1: `vecA=2hati + 3hatj + 6hatk , vecB=hatu + hatj - 2hatk and vecC=hati + 2hatj + hatk` then
`|vecAxx (vecAxx(vecAxxvecB)).vecC|= 243`
Statement 2: `|vecAxx(vecAxx(vecAxxvecB)).vecC|=|vecA|^(2)|[vecA vecB vecC]|`

A

Both the statements are true and statement 2 is the correct explanation for statement 1.

B

Both statements are true but statement 2 is not the correct explanation for statement 1.

C

Statement 1 is true and Statement 2 is false

D

Statement 1 is false and Statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
d
`vecA xx (vecA.vecB) vecA- (vecA.vecA) vecB) .vecC`
`(=underset("zero")ubrace(vecAxx(vecA.vecB)vecA)-(vecA.vecA)xxvecB).vecC`
`=-|vecA|^(2)[vecA vecB vecC]`
now ` |vecA|^(2) = 4+9 + 36 = 49`
`[vecA vecB vecC]=|{:(2,3,6),(1,1,-2),(1,2,1):}|`
2( 1+4) -1 (3 -12) +1 (-6-6)
= 10 +9 -12 =7
`|vecA|^(2) [vecAvecBvecC]|= 49xx 7 = 343`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Comprehension type|27 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Martrix - match type|10 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Exercises MCQ|134 Videos

  • DETERMINANTS

    CENGAGE ENGLISH|Exercise All Questions|264 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Matrix Match Type|5 Videos

Similar Questions

Explore conceptually related problems

Statement 1: vecA=2hati + 3hatj + 6hatk , vecB=hati + hatj - 2hatk and vecC=hati + 2hatj + hatk then |vecAxx (vecAxx(vecAxxvecB)).vecC|= 243 Statement 2: |vecAxx(vecAxx(vecAxxvecB)).vecC|=|vecA|^(2)|[vecA vecB vecC]|

If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2hatk , then [veca vecb vecc]=

If veca=2hati+3hatj+hatk, vecb=hati-2hatj+hatk and vecc=-3hati+hatj+2hatk , then [veca vecb vecc]=

If veca=2hati-3hatj-hatk and vecb=hati+4hatj-2hatk , then vecaxxvecb is

If veca=7hati+3hatj-5hatk, vecb=2hati+5hatj-hatk and vecc-hati+2hatj+4hatk, then verify that vecaxx(b+c)=vecaxxvecb+vecaxxvecc

If veca=7hati+3hatj-6hatk , vecb=2hati+5hatj-hatk and vecc=-hati+2hatj+4hatk . Find (veca-vecb)xx(vecc-vecb) .

If vecA 2 hati +hatj -hatk, vecB=hati +2hatj +3hatk, vecC=6hati -2hatj-6hatk angle between (vecA+vecB) and vecC will be

Given the vector vecA=2hati+3hatj-hatk, vecB=3hati-2hatj-2hatk & vecC=phati+phatj+phatk . Find the angle between (vecA-vecB) &vecC

If veca=2hati+2hatj-hatk, vecb=3hati-hatj-hatk and vecc=hati+2hatj-3hatk then verify that vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc .

if veca=hati-hatj-3hatk, vecb=4hati-3hatj+hatk and vecc=2hati+hatj+2hatk, verify that vecaxx(vecb+vecc)=vecaxxvecb+vecaxxvecc