Create a question about the chapter vectors(it should be original yet difficult) and also provide the answer the best question with the best difficulty will get brainliest
Answers
Important Questions & Answers For Class 12 Maths Chapter 10 Vector Algebra
Q. No. 1: Represent graphically a displacement of 40 km, 30° east of north.
Solution:
Class 12 Chapter 10 Imp Ques. 1 figure 1
Hence, the vector OP→ represents the displacements of 40 km, 30° east of north.
Q. No. 2: Find the unit vector in the direction of the sum of the vectors a⃗ =2i^−j^+2k^ and b⃗ =−i^+i^+3k^.
Solution:
Let c⃗ be the sum of a⃗ and b⃗ .
Class 12 Chapter 10 Imp Ques. 2 figure 1
The unit vector is:
Class 12 Chapter 10 Imp Ques. 2 figure 2
Q. No. 3: Find the vector joining the points P(2, 3, 0) and Q(– 1, – 2, – 4) directed from P to Q.
Solution:
Since the vector is to be directed from P to Q, clearly P is the initial point and Q is the terminal point.
P(2, 3, 0) = (x1, y1, z1)
Q(-1, -2, -4) = (x2, y2, z2)
Vector joining the points P and Q is:
Class 12 Chapter 10 Imp Ques. 3 figure 1
Q. No. 4: Find a vector in the direction of a vector 5i^−j^+2k^
which has a magnitude of 8 units.
Solution:
Let a⃗ =5i^−j^+2k^
Class 12 Chapter 10 Imp Ques. 4 figure 1
Hence, the vector in the direction of vector 5i^−j^+2k^ which has a magnitude of 8 units is given by
Class 12 Chapter 10 Imp Ques. 4 figure 2
Q. No. 5: Show that the vector i^+j^+k^ is equally inclined to the axes OX, OY and OZ.
Solution:
Let a⃗ =i^+j^+k^
Class 12 Chapter 10 Imp Ques. 5 figure 1
Therefore, the direction cosines of a⃗ are (1/√3, 1/√3, 1/√3).
Let α, β, γ be the angles formed by a⃗ with the positive directions of x, y, and z-axes.
Then,
cos α = 1/√3, cos β = 1/√3 cos γ = 1/√3
Hence, the given vector is equally inclined to axes OX, OY and OZ.
Q. No. 6: Show that the points A, B and C with position vectors a⃗ =3i^−4j^−4k^, b⃗ =2i^−j^+k^ and c⃗ =i^−3j^−5k^ form the vertices of a right-angled triangle.
Solution:
Position vectors of points A, B and C are respectively given as below.
a⃗ =3i^−4j^−4k^, b⃗ =2i^−j^+k^ and c⃗ =i^−3j^−5k^
Class 12 Chapter 10 Imp Ques. 6 figure 1
Therefore, ABC is a right-angled triangle.