NCERT Class 12-Mathematics: Chapter – 10 Vector Algebra Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 13:

The angle between the vectors and is

(A)

(B)

(C)

(D)

Answer:

(B) is the correct answer. Apply the formula .

Question 14:

The value of for which the two vectors and are perpendicular is

(A)

(B)

(C)

(D)

Answer:

(D) Is the correct answer.

Question 15:

The area of the parallelogram whose adjacent sides are and is

(A)

(B)

(C)

(D)

Answer:

(B) Is the correct answer.

Area of the parallelogram whose adjacent sides are is .

Question 16:

If and , the value is

(A)

(B)

(C)

(D) None of these

Answer:

(C) Is the correct answer.

Using the formula .

Therefore,

Question 17:

The 2 vectors represents the two sides AB and AC, respectively of a ΔABC. The length of the median through A is

(A)

(B)

(C)

(D) None of these

Answer:

(A) Is the correct answer.

Median is given by

Question 18:

The projection of vector along is

(A)

(B)

(C)

(D)

Answer:

(A) Is the correct answer.

Projection of a vector is

Question 19:

If and are unit vectors, then what is the angle between and for to be a unit vector?

(A)

(B)

(C)

(D)

Answer:

(A) Is the correct answer.

We have