The points 2bar(a)+3bar(b)+bar(c), bar(a...

The points `2bar(a)+3bar(b)+bar(c), bar(a)+bar(b), 6bar(a)+11bar(b)+5bar(c)` are

Collinear

Coplanar but non collinear

non coplanar

cannot be determined

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If bar(a), bar(b), bar(c) are non coplanar then the vectors bar(a)-2bar(b)+3bar(c), -2bar(a)+3bar(b)-4bar(c), bar(a)-3bar(b)+5bar(c) are

If bar(a), bar(b), bar(c) are linearly independent vectors, then show that bar(a)-3bar(b)+2bar(c), 2bar(a)-4bar(b)-bar(c), 3bar(a)+2bar(b)-bar(c) are linearly independent.

If bar(a), bar(b), bar(c) are non coplanar, show that the vectors bar(a)+2bar(b)-bar(c), 2bar(a)-3bar(b)+2bar(c), 4bar(a)+bar(b)+3bar(c) are linearly independent.

Show that the following vectors are linearly dependent bar(a)-2bar(b)+bar(c), 2bar(a)+bar(b)-bar(c), 7bar(a)-4bar(b)+bar(c) where bar(a), bar(b), bar(c) are non-coplanar vectors

Find a linear relation between the vectors bar(a)+3bar(b)+4bar(c), bar(a)-2bar(b)+3bar(c), bar(a)+5bar(b)-2bar(c) and 6bar(a)+14bar(b)+4bar(c)" where "bar(a), bar(b), bar(c) are non coplanar vectors.

S.T the points whose P.V are bar(a) - 2bar(b) + 3bar(c ), 2bar(a)+3bar(b)-4bar(c ), -7bar(b)+10bar(c ) are collinear.

Prove that the following four points are coplanar. i) 4bar(i)+5bar(j)+bar(k), -bar(j)-bar(k), 3bar(i)+9bar(j)+4bar(k), -4bar(i)+4bar(j)+4bar(k) ii) -bar(a)+4bar(b)-3bar(c), 3bar(a)+2bar(b)-5bar(c), -3bar(a)+8bar(b)-5bar(c), -3bar(a)+2bar(b)+bar(c)" ("bar(a), bar(b), bar(c) are non-coplanar vectors) iii) 6bar(a)+2bar(b)-bar(c), 2bar(a)-bar(b)+3bar(c), -bar(a)+2bar(b)-4bar(c), -12bar(a)-bar(b)-3bar(c)" ("bar(a), bar(b), bar(c) are non-coplanar vectors)

i) If bar(a), bar(b), bar(c) are non coplanar vectors, then prove that the vectors 5bar(a)-6bar(b)+7bar(c), 7bar(a)-8bar(b)+9bar(c) and bar(a)-3bar(b)+5bar(c) are coplanar.

AAKASH SERIES-PROPERTIES OF VECTORS-EXERCISE - II

The position vector of a point lying on the line joining the points wh...
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The points with P.V's bar(i)+2bar(j)+bar(k), 2bar(i)+3bar(j)+4bar(k) a...
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The points 2bar(a)+3bar(b)+bar(c), bar(a)+bar(b), 6bar(a)+11bar(b)+5ba...
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i) If bar(a), bar(b), bar(c) are non coplanar vectors, then prove that...
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If bar(a), bar(b), bar(c) are non coplanar then the vectors bar(a)-2ba...
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The vectors 2bar(i)-3bar(j)+bar(k), bar(i)-2bar(j)+3bar(k), 3bar(i)+ba...
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Let bar(a)=bar(i)+bar(j), bar(b)=bar(j)+bar(k) and bar(c)=alphabar(a)+...
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The number of distinct real values of lambda for which the vectors -la...
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If bar(a)=bar(i)+bar(j)+bar(k), bar(b)=4bar(i)+3bar(j)+4bar(k), bar(c)...
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If bar(a)=2bar(i)-bar(j)+3bar(k), bar(b)=-bar(i)+4bar(j)-2bar(k), bar(...
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If the points A(bar(a)), B(bar(b)), C(bar(c)) satisfy the relation 3ba...
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If xbar(a)+ybar(b)+zbar(c),xbar(b)+ybar(c)+zbar(a),xbar(c)+ybar(a)+zba...
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If bar(r)=3bar(i)+2bar(j)-5bar(k), bar(a)=2bar(i)-bar(j)+bar(k), bar(b...
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The vector of magnitude 3sqrt(6) along the bisector of the angle betwe...
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The vector abar(i)+b""bar(j)+cbar(k) is a bisector of the angle betwee...
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If the vector -bar(i)+bar(j)-bar(k) bisects the angles between the vec...
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If A(1, -1, -3), B(2, 1, -2), C(-5, 2, -6) are the vertices of a Delta...
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The median AD of the triangle ABC is bisected at E. BE meets AC in F t...
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If S is the circumcentre, G the centroid, O the orthocentre of Delta A...
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If S is the circumcentre, O is the orthocentre of Delta ABC then vec(O...
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