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Vector Algebra

Short Answer Type

111. Show that the three points A (1, –2, –8) , B (5. 0. –2) and C (11, 3. 7) are collinear and find the ratio in which B divides AC.

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112. If Q is the point of intersection of the medians of the triangle ABC, then prove that

QA with rightwards arrow on top space plus space QB with rightwards arrow on top space plus space QC with rightwards arrow on top space equals space 0 with rightwards arrow on top.

91 Views

113. ABCD is a parallelogram. E, F are mid-points of BC, CD respectively. AE, AF meet the diaginal BD at Q, P respectively. Show that PQ trisects DB.

89 Views

114. If

straight a with rightwards arrow on top comma space straight b with rightwards arrow on top comma space stack straight c comma with rightwards arrow on top straight d with rightwards arrow on top

are any four vectors in 3 - dimensional space with the same initial point and such that

3 space straight a with rightwards arrow on top space space minus space 2 space straight b with rightwards arrow on top space plus space straight c with rightwards arrow on top space minus space 2 space straight d with rightwards arrow on top space equals space 0 with rightwards arrow on top comma space

show that terminals, A, B, C, D of these vectors are coplanar. Find the point at which AC and BD meet. Find the ratio in which P divides AC and BD.

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115. Four points A, B, C, D with position vectors

straight a with rightwards arrow on top comma space straight b with rightwards arrow on top comma space straight c with rightwards arrow on top comma space straight d with rightwards arrow on top

respectively are such that

3 straight a with rightwards arrow on top space minus space straight b with rightwards arrow on top space plus space space 2 straight c with rightwards arrow on top space minus space 4 space straight d with rightwards arrow on top space equals space 0 with rightwards arrow on top

. Show that the four points are coplanar. Also, find the position vector of the point of intersection of lines AC and BD.

91 Views

Long Answer Type

116. The mid-points of two opposite sides of a quadrilateral and the mid-points of the diagonals are the vertices of a parallelogram. Prove using vectors.

89 Views

Short Answer Type

117. A point P divides a line segment AB in the ratio A : 1. Give the values of A for which
P lies in between AB and
(i) nearer A than B (ii) nearer B than A

Since P lies in between AB and P is nearer A than B.

therefore space space space space AP space less than thin space BP space space space straight i. straight e. space AP over BP less than 1 therefore space space space straight lambda space less than space 1. space space space Also space straight lambda space greater than 0 therefore space space space 0 space less than space straight lambda space less than space 1.

If P is nearer to B than A, then

AP greater than BP space space straight i. straight e. space space AP over BP greater than 1 space comma space space straight i. straight e. space space space space straight lambda space greater than space 1.

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118. A point P divides a line segment AB in the ratio A : 1. Give the values of A for which P lies outside AB and
(i) nearer A than B (ii) nearer B than A.

78 Views

Long Answer Type

119. Show that the lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.

97 Views

120. Show that a quadrilateral is a parallelogram if an only if diagonals bisect each other.

90 Views

Previous Year Papers

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Short Answer Type

Long Answer Type

Short Answer Type

117. A point P divides a line segment AB in the ratio A : 1. Give the values of A for whichP lies in between AB and (i) nearer A than B (ii) nearer B than A

Long Answer Type

117. A point P divides a line segment AB in the ratio A : 1. Give the values of A for which
P lies in between AB and
(i) nearer A than B (ii) nearer B than A