Question

If a vector 2i +3j+8k is perpendicular to the vector 4i +4j+ ak,then the value of a is

Answer 1

Answer:

Given:

2 vectors are provided such as

1. 2i + 3j + 8k

2. 4i + 4j + ak

To find:

Value of "a"

Concept:

Whenever 2 vectors are perpendicular, their scalar product (dot product) is zero.

Always use this property to solve this kind of questions

Formulas used:

Let the vectors be A and B

A . B = 0

Calculation:

A . B = 0

=> (2i + 3j + 8k).(4i + 4j + ak) = 0

=> 8 + 12 + 8a = 0

=> 8a = -20

=> a = - 5/2 = -2.5

=> a = -2.5

so value of "a" is -2.5.

Answer 2

Given :-----

• vector A = 2i + 3j + 8k
• vector B = 4i + 4j + ak
• Both are perpendicular to each other ..

To Find :----

• Value of A ?

concept used :----

• Two vectors A and B are perpendicular if and only if their scalar product is equal to zero.....

$\huge{\mathfrak{\green{S}}}{\mathfrak{o}}{\mathfrak{\orange{l}}}{\mathfrak{\red{u}}}{\mathfrak{\pink{t}}}{\mathfrak{\purple{i}}}{\mathfrak{\blue{o}}}{\mathfrak{\red{n}}}$ :-------

(2i + 3j + 8k)(4i + 4j + ak) = 0

→ (2×4) + (3×4) + (8×a) = 0

→ 8 + 12 + 8a = 0

→ 8a = (-20)

→ a = (-20)/8

→ a = (-5)/2

→ a = (-2.5)

(Hope it helps you)

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Extra Brainly knowledge :----

→ Two vectors A and B are parallel if and only if they are scalar multiples of one another.

A = k×B [k is a constant not equal to zero.]