Find the vector from the origin O to the centroid of the triangl

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsShort Answer Type

101.

If straight a with rightwards arrow on top space equals straight b with rightwards arrow on top space plus space straight c with rightwards arrow on top,  then is true that open vertical bar straight a with rightwards arrow on top close vertical bar space equals space open vertical bar straight b with rightwards arrow on top close vertical bar space plus space open vertical bar straight c with rightwards arrow on top close vertical bar space ? Justify your answer.

80 Views

 Multiple Choice QuestionsMultiple Choice Questions

102. In triangle ABC, which of the following is not true

  • AB with rightwards arrow on top space plus space BC with rightwards arrow on top space plus space CA with rightwards arrow on top space equals space 0 with rightwards arrow on top
  • AB with rightwards arrow on top space plus space BC with rightwards arrow on top space minus space AC with rightwards arrow on top space equals space 0 with rightwards arrow on top
  • AB with rightwards arrow on top space plus space BC with rightwards arrow on top space minus space CA with rightwards arrow on top space equals space 0 with rightwards arrow on top
  • AB with rightwards arrow on top space plus space BC with rightwards arrow on top space minus space CA with rightwards arrow on top space equals space 0 with rightwards arrow on top
99 Views

103.

If straight a with rightwards arrow on top and straight b with rightwards arrow on top are two collinear vectors, then which of the following are incorrect:

  • straight b with rightwards arrow on top equals space straight lambda space straight a with rightwards arrow on top comma space space for space some space scalar space straight lambda
  • straight a with rightwards arrow on top space equals plus-or-minus space straight b with rightwards arrow on top
  • the respective components of straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are proportional

  • the respective components of straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are proportional

123 Views

104.

If straight a with rightwards arrow on top is a non-zero vector of magnitude ‘a’ and λ a non-zero scalar, then straight lambda straight a with rightwards arrow on top is a unit vector if

  • straight lambda space equals space 1
  • straight lambda equals negative 1
  • straight a space equals space open vertical bar straight lambda close vertical bar
  • straight a space equals space open vertical bar straight lambda close vertical bar
87 Views

Advertisement

 Multiple Choice QuestionsShort Answer Type

105. Find the position vector of a point R which divides the line joining straight P left parenthesis 3 straight a with rightwards arrow on top space minus space 2 space straight b with rightwards arrow on top right parenthesis space and space straight Q left parenthesis straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top right parenthesis in the ratio 2 : 1 
(i) internally and (ii) externally.
86 Views

106. Find the position vector of a point R which divides the line joining two points straight P left parenthesis 2 straight a with rightwards arrow on top space plus space straight b with rightwards arrow on top right parenthesis space and space straight Q left parenthesis straight a with rightwards arrow on top space minus space 3 space straight b with rightwards arrow on top right parenthesis externally in the ratio 1 :2. Also, show that P is the middle point of the line segment RQ.
83 Views

 Multiple Choice QuestionsLong Answer Type

107. Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are straight i with hat on top space plus space 2 space straight j with hat on top space minus space straight k with hat on top and negative straight i with hat on top space plus space straight j with hat on top space plus space straight k with hat on top respectively, in the ratio 2 : 1
(i) internally                  (ii) externally
78 Views

 Multiple Choice QuestionsShort Answer Type

108.

If straight a with rightwards arrow on top an straight b with rightwards arrow on top are position vectors of points A and B respectively, then find the position vector of points of trisection of AB.

175 Views

Advertisement
109. Find the position vector of the mid-point of the vector joining the points P (2, 3, 4) and Q(4, 1, – 2).
91 Views

Advertisement

110. Find the vector from the origin O to the centroid of the triangle whose vertices are (1, – 1, 2), (2, 1, 3) and (–1, 2, –1).


Let straight a with rightwards arrow on top space equals space straight i with hat on top space minus space straight j with hat on top space plus space 2 space straight k with hat on top comma space space space straight b with rightwards arrow on top space equals space 2 space straight i with hat on top space plus space straight j with hat on top space plus space 3 space straight k with hat on top comma space space straight c with rightwards arrow on top space equals space minus straight i with hat on top space plus space 2 space straight j with hat on top space minus space straight k with hat on top be the position vectors of vertices A, B, C respectively. 
Position vector straight d with rightwards arrow on top of centroid is given by
 straight d with rightwards arrow on top space equals space fraction numerator straight a with rightwards arrow on top plus straight b with rightwards arrow on top plus straight c with rightwards arrow on top over denominator 3 end fraction
space space space space space space equals space fraction numerator left parenthesis straight i with hat on top space minus space straight j with hat on top space plus space 2 space straight k with hat on top right parenthesis space plus space left parenthesis 2 space straight i with hat on top space space plus space straight j with hat on top space plus 3 space straight k with hat on top right parenthesis space plus space left parenthesis negative straight i with hat on top space plus space 2 space straight j with hat on top space minus space straight k with hat on top right parenthesis over denominator 3 end fraction space equals space fraction numerator 2 stack straight i space with hat on top plus 2 space straight j with hat on top space plus space 4 space straight k with hat on top over denominator space 3 end fraction

87 Views

Advertisement
Advertisement