Plus Two Maths Chapter Wise Previous Questions Chapter 10 Vector Algebra are part of Plus Two Maths Chapter Wise Previous Year Questions and Answers. Here we have given Plus Two Maths Chapter Wise Previous Chapter 10 Vector Algebra.
Kerala Plus Two Maths Chapter Wise Previous Questions Chapter 10 Vector Algebra
Plus Two Maths Vector Algebra 3 Marks Important Questions
Question 1.
(i) With help of a suitable figure for any three vectorsa,bandc show that (ˉa+ˉb)+ˉc=ˉa+(→b+ˉc)
(ii) If ˉa = i – j + k and ˉb = 2i – 2j – k. What is the projection of a on b? (March – 2011)
Answer:
(i) Answered in previous years questions
No. 1(ii) (6 Mark question)
(ii) Projection of ˉa on ˉb=ˉa⋅ˉb|ˉb|=2+2−1√4+4+1=1
Question 2.
(i) If ˉa = 3i – j – 5k and ˉb = i – 5j + 3k Show that ˉa + ˉb and a bare perpendicular.
(ii) Given the position vectors of three points as A(i – j + k); B(4i + 5j + 7k) C(3i + 3j + 5k)
(a)Find ¯AB and ¯BC
(b) Prove that A,B and C are collinear points. (March – 2011)
Answer:
Question 3.
(i) Write the unit vector in direction of i + 2j – 3k.
(ii) If ¯PQ = 31 + 2j — k and the coordinate of P are(1, -1,2) , find the coordinates of Q. (May – 2012)
Answer:
Question 4.
(a) The angle between the vectors ˉa and ˉb such that |→a|=|ˉb|=√2
ˉa.ˉb = 1 is
(i) π2 (ii) π3 (iii) π4 (iv) 0
(b) Find the unit vector along ˉa−ˉb where ˉa = i + 3j – k and ˉb 3i + 2j + k (March -2016)
Answer:
Plus Two Maths Vector Algebra 4 Marks Important Questions
Question 1.
Consider the vectors ˉa = 21+ j – 2k and ˉb = 6i – 3j + 2k.
(i) Find ˉaˉb and ˉa×ˉb.
(ii) Verity that |ˉa×ˉb|=|→a|2|ˉb|2−(ˉa⋅ˉb)2 (March – 2012)
Answer:
Question 2.
(i) For any three vectors ˉa,ˉb,ˉc, show that ˉa×(ˉb+ˉc)+ˉb×(ˉc+ˉa)+ˉc×(ˉa+ˉb)=0
(ii) Given A (1, 1, 1), B (1, 2, 3), C (2, 3, 1) are the vertices of MBCa triangle. Find the area of the ∆ABC (May – 2012)
Answer:
Question 3.
Consider A (2, 3, 4) , B (4, 3, 2) and C (5, 2, -1) be any three points
(i) Find the projection of ¯BC on ¯AB
(ii) Find the area of triangle ABC (March – 2013)
Answer:
Question 4.
(i) Find the angle between the vectors ˉa =3i + 4j + k and ˉb = 2i + 3j – k
(ii) The adjacent sides of a parallelogram are ˉa = 3i + λj + 4k and ˉb = i – λj + k
(a) Find ˉa×ˉb
(b) If the area of the parallelogram is square units, find the value of A (May – 2013)
Answer:
Question 5.
Let ˉa = 2i – j + 2k and ˉb = 6i + 2j + 3k
(i) Find a unit vector in the direction of ˉa + ˉb
(ii) Find the angle between a and b (March – 2014)
Answer:
Question 6.
Consider the triangle ABC with vertices A(1, 1, 1) , B (1, 2, 3) and C (2, 3, 1)
(i) Find ¯AB and ¯AC
(ii) Find ¯AB x ¯AC
(iii) Hence find the area of the triangle (March – 2014)
Answer:
Question 7.
Consider the vectors ˉa = i – 7j + 7k; ˉb = 3i – 2j + 2k
(a) Find ¯ab.
(b) Find the angle between ˉa and ˉb.
(c) Find the area of parallelogram with adjacent sides ˉa and ˉb. (May – 2014)
Answer:
Question 8.
(a) If the points A and B are (1, 2, -1) and (2, 1, -1) respectively, then is
(i) i + J
(ii) i – J
(iii) 2i + j – k
(iv) i + j + k
(b) Find the value of for which the vectors 2i – 4j + 5k, i – λj + k and 3i + 2j – 5k are coplanar.
(c) Find the angle between the vectors a = 2i + j – k and b = i – j + k (March – 2016)
Answer:
Question 9.
(i) (ˉa−ˉb)×(ˉa+ˉb) is equaito
(a) ˉa (b) |ˉa|2−|ˉb|2 (c) ˉa×ˉb (d) 2(ˉa×ˉb)
(ii) If ˉa and ˉb are any two vectors, then
(ˉa×ˉb)2=|ˉa⋅ˉaˉa⋅ˉbˉa⋅ˉbˉbˉb|
(iii) Using vectors, show that the points A(1, 2, 7), B(2, 6, 3), C(3, 10, -i) are collinear. (May – 2016)
Answer:
Plus Two Maths Vector Algebra 6 Marks Important Questions
Question 1.
(i) Find a vector in the direction of ˉr = 3E – 4j that has a magnitude of 9.
(ii) For any three vectors ¯a,b and ˉc, and Prove that (ˉa+ˉb)+ˉc=ˉa+(ˉb+ˉc).
(iii) Find a unit vector perpendicular to ˉa+ˉb and ˉa−ˉb, where ˉa = i – 3j + 3k and ˉb and /barc = 3E—3j+2k. (March – 2010)
Answer:
(i) Unit vector of magnitude 9
Question 2.
Let A(2, 3, 4), B(4, 3, 2) and C(5, 2, -1) be three points
(i) Find ¯AB and ¯BC
(ii) Find the projection of ¯BC on ¯AB
(iii) Fiñd the area of the triangle ABC. (May – 2010)
Answer:
Question 3.
ABCD s a parallelogram with A as the origin, ˉb and ˉd are the position vectors of B and D respectively.
(i) What is the position vector of C?
(ii) What is the angle between ¯AB and ¯AD?
(iii) If |→AC|=|→BD|, show that ABCD is a rectangle. (May – 2011)
Answer:
(i) Since ABCD is a parallelogram with A as the
Question 4.
(a) If ˉa,ˉb,ˉc,ˉd respectively are the position vectors representing the vertices A,B,C,D of a parallelogram, then write /bard in terms of ˉa,ˉb,ˉc.
(b) Find the projection vector of /barb = i + 2j + k along the vector /bara = 21 – i – j + 2k. Also write /barb as the sum of a vector along /bara and a perpendicular to /bara.
(C) Find the area of a parallelogram for which the vectors 21 + j, 31 + j +4k are adjacent sides. (March – 2015)
Answer:
Question 5.
(a) Write the magnitude of a vector /bara in terms of dot product.
(b) If ˉa,ˉb,ˉa+ˉb are unit vectors, then prove that the angle between /bara and /barb is 2π3
(c) If 2i + j – 3k and mi + 3j – k are perpendicular to each other, then find ‘m’.
Also find the area of the rectangle having these two vectors as sides. (March – 2015)
Answer:
Question 6.
Consider the triangle ABC with vertices A(1, 2, 3), B(-1, 0, 4), C(0, 1, 2)
(a) Find ¯AB and ¯AC
(b) Find ∠A
(c) Find the area of triangle ABC. (May – 2015)
Answer:
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