Home
Class 12
MATHS
bar(a),bar(b),bar(c) are three non-copla...

`bar(a),bar(b),bar(c)` are three non-coplanar vectors.
If `bar(p)=(bar(b)xxbar(c))/(bar(a)*(bar(b)xxbar(c))),bar(q)=(bar(c)xxbar(a))/(bar(a)*(bar(b)xxbar(c))),bar(r)=(bar(a)xxbar(b))/(bar(a)*(bar(b)xxbar(c)))`,
show that `bar(a)*bar(p)+bar(b)*bar(q)+bar(c)*bar(r)=3`.

Text Solution

Verified by Experts

We use results : If in a scalar triple product, two vectors are equal, then the scalar triple product is zero and
`bar(a)*(bar(b)xxbar(c))=bar(b)*(bar(c)xxbar(a))=bar(c)*(bar(a)xxbar(b))`.
`:.bar(a)*bar(p)+bar(b)*bar(q)+bar(c)*bar(r)=bar(a)*((bar(b)xxbar(c))/(bar(a)*(bar(b)xxbar(c))))+bar(b)*((bar(c)xxbar(a))/(bar(a)*(bar(b)xxbar(c))))+bar(c)*((bar(a)xxbar(b))/(bar(a)*(bar(b)xxbar(c))))`
`=(bar(a)*(bar(b)xxbar(c)))/(bar(a)*(bar(b)xxbar(c)))+(bar(b)*(bar(c)xxbar(a)))/(bar(a)*(bar(b)xxbar(c)))+(bar(c)*(bar(a)xxbar(b)))/(bar(a)*(bar(b)xxbar(c)))`
`=([bar(a)bar(b)bar(c)])/([bar(a)bar(b)bar(c)])+([bar(a)bar(b)bar(c)])/([bar(a)bar(b)bar(c)])+([bar(a)bar(b)bar(c)])/([bar(a)bar(b)bar(c)])=3`
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Theory Questions|4 Videos

  • VECTORS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Examples for Practics|28 Videos

  • TRIGONOMETRIC FUNCTIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Multiple Choice Questions|12 Videos

Similar Questions

Explore conceptually related problems

bar(a)xx(bar(b)xxbar(c))+bar(b)xx(bar(c)xxbar(a))+bar(c)xx(bar(a)xxbar(b))=

If bar(a),bar(b),bar(b),bar(c) are three non coplanar vectors bar(p)=(bar(b)xxbar(c))/([bar(a)bar(b)bar(c)]),bar(q)=(bar(c)xxbar(a))/([bar(a)bar(b)bar(c)]),bar(r)=(bar(a)xxbar(b))/([bar(a)bar(b)bar(c)]) then (2bar(a)+3bar(b)+4bar(c))*bar(p)+(2bar(b)+3bar(c)+4bar(a))bar(q)+(2bar(c)+3bar(a)+4bar(b))*bar(r)=

If bar(a),bar(b),bar(c) are three non coplanar vectors bar(p)=((bar(b)xxbar(c)))/([bar(a)bar(b)bar(c)]),bar(q)=(bar(c)xxbar(a))/([bar(a)bar(b)bar(c)]),bar(r)=(bar(a)xxbar(b))/([bar(a)bar(b)bar(c)]) then (2bar(a)+3bar(b)+4bar(c))*bar(p)+(2bar(b)+3bar(c)+4bar(a))*bar(q)+(2bar(c)+3bar(a)+4bar(b))*bar(r)

If [bar(a)bar(b)bar(c)]!=0andbar(p)=(bar(b)xxbar(c))/([bar(a)bar(b)bar(c)]),bar(q)=(bar(c)xxbar(a))/([bar(a)bar(b)bar(c)]),bar(r)=(bar(a)xxbar(b))/([bar(a)bar(b)bar(c)]) , then bar(a)*bar(p)+bar(b)*bar(q)+bar(c)*bar(r) is equal to

bar(i)xx(bar(a)xxvec i)+bar(j)xx(bar(a)xxbar(j))+(bar(a)xx(bar(a)xxbar(j))+bar(k)(bar(a)xxbar(k))=

If (bar(b)xxbar(c))xx(bar(c)xxbar(a))=3bar(c) then [bar(b)xxbar(c)bar(c)xxbar(a)bar(a)xxbar(b)]=

(bar(a)xxbar(i))(bar(b)xxbar(i))+(bar(a)xxbar(j))(bar(b)xxbar(j))+(bar(a)xxbar(k))(bar(b)xxbar(k))=

If [bar(a)bar(b)bar(c)]=1 then (bar(a)(bar(b)xxbar(c)))/((bar(c)xxbar(a))*bar(b))+(bar(b)*(bar(c)xxbar(a)))/((bar(a)xxbar(b))*bar(c))+(bar(c)(bar(a)xxbar(b)))/((bar(b)xxbar(c))*bar(a))

(bar(a)+bar(b))xx(bar(a)-bar(b))+(bar(b)+bar(c))xx(bar(b)-bar(c))+(bar(c)+bar(a))xx(bar(c)-bar(a))=

If bar(a),bar(b),bar(c) are non-coplanar vectors such that then bar(b)xxbar(c)=bar(a),bar(c)xxbar(a)=bar(b) and bar(a)xxbar(b)=bar(c), then |bar(a)+bar(b)+bar(c)|=