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Scalar Or Dot Product Maths - Scalar Or Dot Product

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 144 questions in this chapter.

Question types

Scalar Or Dot Product question types

144 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

144
Questions
4
Question groups
5
Question types
Sample Questions

Scalar Or Dot Product questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
If $\vec{\text{a}}$ and $\vec{\text{b}}$ are unit vectors,then the greatest value of $\sqrt{3}\big|\vec{\text{a}}+\vec{\text{b}}\big|+\big|\vec{\text{a}}-\vec{\text{b}}\big|$ is:
  1. $2$
  2. $2\sqrt{2}$
  3. $4$
  4. $\text{None of these}$
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Q 2M.C.Q (1 Marks)1 Mark
If the vectors $\hat{\text{i}}-2\text{x}\hat{\text{j}}+3\text{y}\hat{\text{k}}$ and $\hat{\text{i}}+2\text{x}\hat{\text{j}}-3\text{y}\hat{\text{k}}$ are perpendicular, then the locus of (x,y) is:
  1. A circle.
  2. An ellipse.
  3. A hyperbola.
  4. None of these.
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Q 3M.C.Q (1 Marks)1 Mark
What is the length of the longer diagonal of the parallelogram constructed on $5\vec{\text{a}}+2\vec{\text{b}}$ and $\vec{\text{a}}-3\vec{\text{b}}$ if it is given that $|\vec{\text{a}}|=2\sqrt{2},\big|\vec{\text{b}}\big|=3$ and the angle between $\vec{\text{a}}$ and $\vec{\text{b}}$ is $\frac{\pi}{4}$?
  1. $15$
  2. $\sqrt{113}$
  3. $\sqrt{593}$
  4. $\sqrt{369}$
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Q 4M.C.Q (1 Marks)1 Mark
If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are any three mutualy perpendicular vectors of equal magnitude a, then $\big|\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big|$ is equal to
  1. $\text{a}$
  2. $\sqrt{2}\text{a}$
  3. $\sqrt{3}\text{a}$
  4. $2\text{a}$
  5. $\text{None of these}$
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Q 62 Marks2 Marks
If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two vectors such that $\big|\vec{\text{a}}\big|=4,\big|\vec{\text{b}}\big|=3$ and $\vec{\text{a}}.\vec{\text{b}}=6,$ find the angle between $\vec{\text{a}}$ and $\vec{\text{b}}$.
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Q 72 Marks2 Marks
Find the angle between the vectora $\vec{\text{a}}=\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}}.$
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Q 82 Marks2 Marks
If the vectors $3\hat{\text{i}}-2\hat{\text{j}}-4\hat{\text{k}}$ and $18\hat{\text{i}}-12\hat{\text{j}}-\text{m}\hat{\text{k}}$ are parallel,  find the value of m.
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Q 92 Marks2 Marks
For any two non-zero vectors, write the value of $\frac{\big|\vec{\text{a}}+\vec{\text{b}}\big|^2+\big|\vec{\text{a}}-\vec{\text{b}}\big|^2}{|\vec{\text{a}}|^2+\big|\vec{\text{b}}\big|^2}.$
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Q 102 Marks2 Marks
Find the angle between the vectors $\vec{\text{a}} $ and $\vec{\text{b}},$ where

$\vec{\text{a}}=\hat {\text{i}}-\hat{\text{j}}$ and $\vec{\text{b}} = \hat{\text{j}}+\hat{\text{k}}$

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Q 113 Marks3 Marks
Write the projection of $\vec{\text{b}}+\vec{\text{c}}$ on $\vec{\text{a}}$ when $\vec{\text{a}}=2\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}},\vec{\text{b}}=\hat{\text{i}}+2\hat{\text{j}}-2\hat{\text{k}}$ and $\vec{\text{c}}=2\hat{\text{i}}-\hat{\text{j}}+4\hat{\text{k}}.$
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Q 123 Marks3 Marks
If $\vec{\text{c}}$ is perpendicular to both $\vec{\text{a}}$ and $\vec{\text{b}},$ then prove that it is perpendicular to both $\vec{\text{a}}+\vec{\text{b}}$ and $\vec{\text{a}}-\vec{\text{b}}.$
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Q 133 Marks3 Marks
Find $\lambda$ when the projection of $\vec{\text{a}}=\lambda\hat{\text{i}}+\hat{\text{j}}+4\hat{\text{k}}$ on $\vec{\text{b}}=2\hat{\text{i}}+6\hat{\text{j}}+3\hat{\text{k}}$ is 4 units.
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Q 143 Marks3 Marks
If a vector$​​\vec{\text{a}}$ is perpendicular to two non-collinear vectors $\vec{\text{b}}$ and $\vec{\text{c}},$ then show that $​​\vec{\text{a}}$ is perpendicular to every vector in the plane of $\vec{\text{b}}$ and $\vec{\text{c}}.$
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Q 153 Marks3 Marks
If the sum of two unit vectors is a unit vector prove that the magnitude of their difference is $\sqrt{3.}$
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Q 174 Marks4 Marks
Prove using vector: the quadrilateral obtained by joining mid-points of adjacent sides of a rectangle is a rhombus.
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Q 184 Marks4 Marks
If either $\vec{\text{a}}=\vec{0}$ or $\vec{\text{b}}=\vec{0},$ then $\vec{\text{a}}.\vec{\text{b}}=0.$ But the converse need not be true. Justify your answer with an example.
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Q 204 Marks4 Marks
(Pythagoras's theorem) Prove by vector method that in a right angleg triang, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
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