The lines barr =bara+ tbarb, barr = barc...

The lines `barr =bara+ tbarb, barr = barc + bart^(1)bard` are coplanar if

`[barc-barabarbbard]=0`

`[barb-bardbarabarc]=0`

`[bara-barbbarcbard]=0`

`[barc-bardbarabarb]=0`

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Observe the following, choose correct answer : Assertion(A): The lines barr =(2bari + barj)+s(bari + barj -bark) and barr =(bari +bark)+t(7bari - barj +bark) are coplanar. Reason (R) : Condition for the lines barr = bara + sbarb and barr = barc + tbard to be coplanar is [bara-barc barb -bard]=0

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Show that the vectors bara - 2barb + 3barc,- 2bara + 3barb - 4barc and bara - 3barb + 5barc are coplanar, where a, b, c are non- coplanar vectors.

The equation of the plane containing the lines barr = bara+ tbarb and barr = barb + sbara is

Show that the four points -bara+ 4barb - 3barc, 3bara +2barb-5barc,-3bara +8barb -5barc and -3bara + 2barb + barc are coplanar, where bara,barb,barc are non - coplanar vectors.

If bara,barb,barc are non-coplanar vectors, prove that barb xx barc, barc xx bara, bara xx barb are also non coplanar and hence express any vector bard in terms of the vectors barbxxbarc, barcxxbara , and baraxxbarb .

If the lines barr=bara+lamda(barbxxbarc) and barr=barb+mu(barcxxbara) intersect each other then the condition is

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AAKASH SERIES-MULTIPLE PRODUCT OF VECTORS-PRACTICE EXERCISE

Let bara ,barb,barc be non coplanar vectors and bara^(1)=(barbxxbarc)/...
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baraxxbara^(1)+barbxxbarb^(1)+barcxxbarc^(1)=
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The vector [(bari-barj)xx(barj-bark)]xx(bari+5bark) is
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Let bara,barb,barc be three vectors which satisfy baraxx(barbxxbarc)=(...
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If bara=bari+barj+bark,bara.barb=1,baraxxbarb=2bari+barj-3bark then 3b...
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Unit vector coplanar with bari+barj+2bark,bari+2barj+bark and perpendi...
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If bara,barc,bard are coplaner then the value of (bard+bara).[baraxx{b...
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Let bara, barb, barc be three vectors having magnitudes 1,1,2 respecti...
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If bara,barb,barc are non-coplanar unit vectors such that baraxx(barbx...
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Vector component of barb perpendicular to bara is
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The vector equation of the plane passing through the points (1, -2, 5)...
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Equation of the plane passing through the points with position vector...
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Vector equation of the plane passing through bara, barb and parallel t...
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The shortest distance between the straight line passing through the po...
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The distance between the plane whose equation is barr · (2bari + barj-...
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The vector equation of a straight line passing through bara and perpen...
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If bara,barb,barc are the position vectors of the vertices of a triang...
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Vector equation of the plane passing through the line barr =bara+ alph...
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The lines barr =bara+ tbarb, barr = barc + bart^(1)bard are coplanar i...
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Let bara=barj-bark and barc= bari -barj-bark. Then the vector barb sat...
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