Question

Two vectors A and B are given by: A = 2i - 3j + 7k and B= -4i + 2j -4k. Find
the dot product (scalar product) of the given two vectors.

Please answer fast!!

Answer 1

A vector quantity is such a quantity that has both magnitude as well as direction as opposed to a scalar quantity which only has a magnitude. For performing calculations with vector quantities a separate branch of mathematics known as vector algebra was formed. Vector algebra deals with the algebraic operations like addition, subtraction, multiplication etc. of vector quantities.

Complete step by step answer:

Letus consider that we have been provided with two vectors a and b such that,

a⃗ =2i+3j+2k

b⃗ =i+j+k

We know that the component of vector a perpendicular to vector b can be obtained by the following expression.

c⃗ =a⃗ −a⃗ ⋅b⃗ ∣∣b⃗ ∣∣2×b⃗.(1)

Where, vector c is the component of vector a perpendicular to the vector b.

The magnitude of vector a is,

|a⃗ |=22+32+22−−−√=17−−√

The magnitude of vec b is,

∣∣b⃗ ∣∣=12+12+12−√=3–√.(2)

The scalar or dot product of vectors a & b is given by,

a⃗ ⋅b⃗ =2(1)−3(1)+2(1)=1..(3)

Now, putting all the values from equations (2) & (3) in equation (1) we get,

c⃗ =2i+3j+2k−1(3–√)2×(i+j+k)

c⃗ =53(i−2j+k)

i.e. 53(i−2j+k) is the vector which is the component of vector a and also perpendicular to vector b.

Hence option (A) is the correct answer option.

Answer 2

Answer:

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