Vector Algebra I Two Marks Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 20
    10 x 2 = 20
  1. If D and E are the midpoints of the sides AB and AC of a triangle ABC, prove that \(\overrightarrow{BE}+\overrightarrow{DC}={3\over2}\overrightarrow{BC}\) .

  2. Find a unit vector along the direction of the vector 5\(\hat{i}\)-3\(\hat{j}\)+4\(\hat{k}\) .

  3. Find the direction cosines of the line joining (2, 3, 1) and (3, - 1, 2).

  4. Verify whether the following ratios are direction cosines of some vector or not\({4\over 3}.0,{3\over 4}\)

  5. Find the direction cosines and direction ratios for the following vectors.5\(\hat{i}\)-3\(\hat{j}\)-48\(\hat{k}\)

  6. If \(\overrightarrow{a}\) and \(\overrightarrow{b}\)are two vectors such that | \(\overrightarrow{a}\) |=10,| \(\overrightarrow{b}\) |=15 and \(\overrightarrow{a}\).\(\overrightarrow{b}\) = 75 \(\sqrt{2}\), find the angle between \(\overrightarrow{a}\)and \(\overrightarrow{b}\).

  7. Find the angle between the vectors  \(2\hat{i}+3\hat{j}-6\hat{k}\) and \(6\hat{i}-3\hat{j}+2\hat{k}\)

  8. Find the area of the parallelogram whose adjacent sides are \(\overrightarrow{a}=3\hat{i}+\hat{j}+4\hat{k}\) and \(\overrightarrow{b}=\hat{i}-\hat{j}+\hat{k}\) .

  9. Classify the following as scalar and vector quantities. (i) time period (ii) distance (iii) force (iv) velocity (v) work done.

  10. If \(\vec{a}=\hat{i}+2\hat{j}+3\hat{k}\) and \(\vec{b}=2\hat{i}+3\hat{j}-5\hat{k}\) then find \(\vec{a} \times \vec{b}\) . Verify that\(\vec{a}\) and \(\vec{b}\) are perpendicular to each other.

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