NCERT Class 12 · Ch 10 Exercise 10.2 · Q12
NCERT Class 12 Maths · Chapter 10 Vector Algebra · Exercise 10.2 Question 12
Find direction cosines of i+2j+3k.
💡 Concept Hints
- Write the vector components and identify the required direction or geometric relation.
- Use the magnitude, dot-product, cross-product or section formula that matches the requested quantity.
✅ Step-by-Step Solution
Final Answer: \(\left[\begin{matrix}\frac{\sqrt{14}}{14}\\\frac{\sqrt{14}}{7}\\\frac{3 \sqrt{14}}{14}\end{matrix}\right]\)
- The direction vector is \(\left[\begin{matrix}1\\2\\3\end{matrix}\right]\), with magnitude √(14)=\(\sqrt{14}\).
- Divide by this nonzero magnitude: \(\left[\begin{matrix}\frac{\sqrt{14}}{14}\\\frac{\sqrt{14}}{7}\\\frac{3 \sqrt{14}}{14}\end{matrix}\right]\).
Master Chapter 10: Vector Algebra
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Vector Algebra.
← Previous Question
Show 2i−3j+4k and −4i+6j−8k are collinear.
Next Question →Find direction cosines from A(1,2,−3) toward B(−1,−2,1).
Related Questions in Vector Algebra
Class 12 Vector Algebra · Mcq Single Correct
Find |a × b|² + (a · b)².
Class 12 Vector Algebra · Mcq Single Correct
Find the area of triangle OAB, where OA = (1,2,3) and OB = (−3,−2,1).
Class 12 Vector Algebra · Mcq Single Correct
For nonzero vectors a,b with angle θ ∈ [0,π], when is a · b ≥ 0?
Class 12 Vector Algebra · Mcq Single Correct
For a vector a, find (a · i)i + (a · j)j + (a · k)k.
Class 12 Vector Algebra · Mcq Single Correct
Which vector has magnitude 9 and the same direction as (1,−2,2)?
Class 12 Vector Algebra · Mcq Single Correct
Find the position vector dividing the segment from 2a − 3b to a + b internally in the ratio…