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Test: Vector Algebra: Dot and Cross Product(22 Nov) - JEE MCQ


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10 Questions MCQ Test - Test: Vector Algebra: Dot and Cross Product(22 Nov)

Test: Vector Algebra: Dot and Cross Product(22 Nov) for JEE 2024 is part of JEE preparation. The Test: Vector Algebra: Dot and Cross Product(22 Nov) questions and answers have been prepared according to the JEE exam syllabus.The Test: Vector Algebra: Dot and Cross Product(22 Nov) MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Vector Algebra: Dot and Cross Product(22 Nov) below.
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Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 1

If | a | = 2, | b | = 5 and | a × b | = 8, thencan be equal to

Detailed Solution for Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 1

Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 2

If  are unit vectors along X-axis, Y-axis and Z-axis respectively, then

Detailed Solution for Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 2

As we know that,

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Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 3

The area of triangle whose adjacent sides are is :

Detailed Solution for Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 3

Area of triangle = ½(a * b)
a = (1, 0, -2)   b = (2, 3, 1)
= i(0 + 6) + j(-4 - 1) + k(3 - 0)
= 6i - 5j + 3k
|a * b| = (36 + 25 + 9)½
|a * b| = (70)½
Area of triangle = ½(a * b)
= [(70)½]/2

Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 4

The value of  is:

Detailed Solution for Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 4

 i.(j * k) + j.(k * i) + k(i * j)
= i.(i) + j.(j) + k.(k)
= 1 + 1 + 1 
= 3

Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 5

The area of parallelogram whose sides areis:​

Detailed Solution for Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 5

A = {(1, -3, 4)}    B = {(3, 1, -2)}
A * B = {(i^(6-4) - j^(-2 -12) + k^ (1+9)} 
= 2i^ + 14j^ + 10k^
Area = [(2)2 + (14)2 + (10)2]½
= (300)½
= 10(3)½ sq unit

Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 6

If   are any two vectors, then

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Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 7

The angle between the vectors is:    is :

Detailed Solution for Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 7

a = 6i - 3j + 2k      b = 2i + j - 2k
a.b = 12 - 3 - 4 = 5
|a| = [(6)2 + (-3)2 + (2)2]1/2 
|a| = [36 + 9 + 4]½
|a| = (49)½
|a| = 7
|b| = [(2)2 + (1)2 + (-2)2]½
|b| = [4 + 1 + 4]½
|b| = 3
Cosθ = (a.b)/|a||b|
= 5/(7)(3)
= 5/21
θ = cos-1(5/21)

Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 8

If  are two vectors, such that , then = ……​

Detailed Solution for Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 8

 |a - b|2 = |a|2 + |b|2 - 2|a||b|
|a - b|2  = (3)2 + (2)2 - 2(5)
|a - b|2  = 9 + 4 - 10
|a - b|2  = 3 
|a - b|   = (3)½.

Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 9

The projection of the vector  on the vector is:​

Detailed Solution for Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 9

Projection = (A.B)/|B|
= [(i + 2j + k) . (2i + 3j + 2k)]/[(2)2 + (3)2 + (2)2]½
= (2 + 6 + 2)/[4 + 9 + 4]½
= 10/(17)1/2

Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 10

The angle between two non-zero vectors  is given by

Detailed Solution for Test: Vector Algebra: Dot and Cross Product(22 Nov) - Question 10

A sequence is a function whose domain is the set of natural numbers or a subset of the natural numbers. We usually use the symbol an to represent a sequence, where n is a natural number and an is the value of the function on n. A sequence may be finite or infinite.

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