The points with P.V's bar(i)+2bar(j)+bar...

The points with P.V's `bar(i)+2bar(j)+bar(k), 2bar(i)+3bar(j)+4bar(k) and 4bar(i)+5bar(j)+10bar(k)` form

An acute angled triangle

obtuse angled triangle

Right angled triangle

collinear

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Find the vector area and area of the triangle with vertices bar(i) + bar(j)-bar(k), 2bar(i)- 3bar(j) + bar(k), 3 bar(i) + bar(j)- 2bar(k) .

The vectors 2bar(i)-3bar(j)+bar(k), bar(i)-2bar(j)+3bar(k), 3bar(i)+bar(j)-2bar(k)

Find the vector equation of the plane passing through the points. 4bar(i)-3bar(j)-bar(k), 3bar(i)+7bar(j)-10bar(k) and 2bar(i)+5bar(j)-7bar(k) and show that the point bar(i) + 2bar(j)-3bar(k) lies in the plane.

The points whose position vectors are 2bar(i)+3bar(j)+4bar(k), 3bar(i)+4bar(j)+2bar(k) and 4bar(i)+2bar(j)+3bar(k) are the vertices of

If the points whose position vectors are 3bar(i) -2bar(j)-bar(k), 2bar(i)+3bar(j)-4bar(k), -bar(i)+bar(j)+2bar(k), 4bar(i)+5bar(j)+lambdabar(k) are coplanar, then show that lambda = -146/17 .

Consider the points A, B, C and D with P.V.'s 7bar(i)-4bar(j)+7bar(k), bar(i)-6bar(j)+10bar(k), -bar(i)-3bar(j)+4bar(k) and 5bar(i)-bar(j)+bar(k) respectively. Then ABCD is a

Write the position vector of the centroid of the triangle formed by the points whose position vectors are 3bar(i)+2bar(j)-bar(k), 2bar(i)-2bar(j)+5bar(k), bar(i)+3bar(j)-bar(k) .

If the point whose position vectors are 3bar(i)-2bar(j)-bar(k), 2bar(i)+3bar(j)-4bar(k), bar(i)+bar(j)-2bar(k), 4bar(i)5bar(j)+lambdabar(k) are coplanar, then show that lambda = -46/7 .

AAKASH SERIES-PROPERTIES OF VECTORS-EXERCISE - II

If the vectors 2i + 3j, 5i + 6j, 8i + lambda j have their initial poin...
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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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