Q1Written answer
Find the unit vector in the direction of sum of vectors
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Given vectors are,
NCERT Exemplar · Class 12 · Maths
Chapter 10: Vector Algebra
Practice each question, then open the answer or worked solution.
Exercise 10.3
Textbook page 215 · 14 questionsQ2Written answer
If find the unit vector in the direction of
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Q3Written answer
Find a unit vector in the direction of where P and Q have co-ordinates (5, 0, 8) and (3, 3, 2), respectively.
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Given coordinates are P(5, 0, 8) and Q(3, 3, 2).
Q4Written answer
If are the position vectors of A and B, respectively, find the position vector of a point C in BA produced such that BC = 1.5 BA.
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Q5Written answer
Using vectors, find the value of k such that the points (k, – 10, 3), (1, –1, 3) and (3, 5, 3) are collinear.
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Let the given points be A(k, – 10, 3), B(1, –1, 3) and C(3, 5, 3).
Q6Written answer
A vector 
is inclined at equal angles to the three axes. If the magnitude of 
is 2√3 units, find
.
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As the vector 
makes equal angles with the axes, their direction cosines should also be same
So, l = m = n
And we know that,
l2 + m2 + n2 = 1 ⇒ l2 + l2 + l2 = 1
3l2 = 1
l = ± 1/√3
Q7Written answer
A vector 
has magnitude 14 and direction ratios 2, 3, – 6. Find the direction cosines and components of
, given that
makes an acute angle with x-axis.
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Solution coming soon.
Q8Written answer
Find a vector of magnitude 6, which is perpendicular to both the vectors 
and 
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Q9Written answer
Find the angle between the vectors
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Q10Written answer
If 
, show that 
. Interpret the result geometrically?
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