Question

vector p is (3i + 2j) and vector q is (4i + 5j). What is the magnitude of the vector we will get by cross product (p x q)​

Answer 1

Answer:

7k  (7 k-cap)

Explanation:

 = p × q

 =  (3i + 2j) × (4i + 5j)

 = 3i(4i + 5j) + 2j(4i + 5j)

 = 12(i×i) + 15(I×j) + 8(j×i) + 10(j×j)

 = 12(0) + 15(k) + 8(-k) + 10(0)

 = 0 + 15k - 8k + 10(0)

 =  7k

Based on:

  i × i = j × j = k × k = 0

  i × j = k   ;  j × k = i   ; k × i = j

  j × i = -k   ;  k × j = -i   ; i × k = -j

Answer 2

Answer:

$\sf\tt\large{\red {\underline {\underline{⚘\;Question:}}}}$

Vector p is (3i + 2j) and vector q is (4i+5j).What is the magnitude of the vector we will get by cross product (p × q).

$\sf\tt\large{\red {\underline {\underline{⚘\;Answer:}}}}$

$\sf\tt\large{\blue {\underline {\underline{\;7k \;(7k \; - cap):}}}}$

$\sf\tt\large{\green {\underline {\underline{⚘\;Solution:}}}}$

Hey mate,

First let verify your questions. And next enter to calculations .

In the question given that the vector p is (3i + 2j) and vector q is (4i + 5j).What is the magnitude of the vector we will get by cross product (p×q).

According to the given question,

we should find magnitude of the vector.

So,

Here,

Put the value of p and q in (p×q) vector.

Multiplying the values of p and we get the value of magnitude .

Now,

$\sf\tt\large{\purple {\underline {\underline{\;= \; ( p × q) vector:}}}}$

$\sf\tt\large{\purple {\underline {\underline{\;= ( 3i + 2j) × ( 4i + 5j):}}}}$

$\sf\tt\large{\purple {\underline {\underline{\;= \; 3i (4i + 5j) +2i (4i + 5j):}}}}$

(Substituting the value of p in q )

= 12 (i × i) + 15 (i × j) +8 (j × i) +10 (j × j)

$\sf\tt\large{\purple {\underline {\underline{\;= \; 12 (0) + 15 (k) +8 (-k)+10 (0):}}}}$

$\sf\tt\large{\purple {\underline {\underline{\;= \;0 + 15k + 8 (-k) + 0:}}}}$

$\sf\tt\large{\purple {\underline {\underline{\;= \;0 + 15k - 8k:}}}}$

$\sf\tt\large{\purple {\underline {\underline{\;= \; 7k}}}}$

So,

Finally we got the value of magnitude of the vector. The value is 7k (7k-cap)

This is the perfect answer to this question.

Hope it helps u mate.

Thank you.