Physics, asked by drshivanarayanreddy, 9 months ago

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

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Answered by havockarthik30
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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.

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