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Applications of Dot Product

Find the scal...

Question

Find the scaler product of vectors $3^i + 4^j - 7^k$ and $5^i + 3^j + 4^k$

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Solution

Scalar product of 2 vectors is its dot product.
$∴ (3^i + 4^j - 7^k) \cdot (5^1 + 3^j + 4^k) = (15 + 12 - 28) = - 1$

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Q. Consider points

A, B, C, D

with position vectors

7^i - 4^j + 7^k

^i - 6^j + 10^k

-^i - 3^j + 4^k

5^i -^j + 5^k

respectively. Then

A B C D

A, B, C, D

with position vector

7^i - 4^j + 7^k

^i - 6^j + 10^k

-^i - 3^j + 4^k

5^i -^j + 5^k

respectively, then

A B C D

Q. Consider the points

A, B, C, D

with position vectors

7^i - 4^j - 7^k

^i - 6^j + 10^k

-^i - 3^j + 4^k

5^i -^j +^k

respectively. Then,

A B C D

2^i + 3^j + 4^k

^i - 4^j + 7^k

are the sides of a parallelogram, then is the vector representing its diagonal.

\to P =^i + 3^j - 7^k

\to Q = 5^i - 2^j + 4^k

then the length of the vector

\to P Q

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