If a vector $2 \hat{i} + 3 \hat{j} + 8 \hat{k}$ is perpendicular to the vector $4 \hat{j} - 4 \hat{i} + α \hat{k}$ , then the value of α is

-1

$\frac{1}{2}$

$- \frac{1}{2}$

1

Solution

$- \frac{1}{2}$

Two vectors must be perpendicular if their dot product is zero.

$let \vec{a} = 2 \hat{i} + 3 \hat{j} + 8 \hat{k} \vec{b} = 4 \hat{j} - 4 \hat{i} + α \hat{k} = - 4 \hat{i} + 4 \hat{j} + α \hat{k} According to the above hypothesis \vec{a} ⊥ \vec{b} \Rightarrow \vec{a} . \vec{b} = 0 \Rightarrow (2 \hat{i} + 3 \hat{j} + 8 \hat{k}) . (- 4 \hat{i} + 4 \hat{j} + α \hat{k}) = 0 \Rightarrow - 8 + 12 + 8 α = 0 \Rightarrow 8 α = - 4 α = - \frac{4}{8} = - \frac{1}{2}$

$\vec{a} . \vec{b} = ab cosθ .$ Here a and b are always positive as they are the magnitudes as $\vec{a} and \vec{b}$ .

Some More Questions From Motion in A Plane Chapter

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
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Motion In A Plane

If a vector $2 \hat{i} + 3 \hat{j} + 8 \hat{k}$ is perpendicular to the vector $4 \hat{j} - 4 \hat{i} + α \hat{k}$ , then the value of α is

-1

$\frac{1}{2}$

$- \frac{1}{2}$

1

Some More Questions From Motion in A Plane Chapter

Give three examples of scalar quantities.

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

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Motion In A Plane

If a vector 2 i^ + 3 j^ + 8 k^ is perpendicular to the vector 4 j^ - 4 i^ + α k^, then the value of α is -1 12 -12 1

Some More Questions From Motion in A Plane Chapter

Give three examples of scalar quantities.

Give three examples of vector quantities.

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

Is a physical quantity, having a direction, necessarily a vector?

Name a quantity which is both scalar as well as vector.

Which of the followings is/are vector quantities: work, power, acceleration, mass, momentum?

Pick up the odd one from the following: force, linear momentum, mass, impulse.

Pick out the only vector quantities in the following list:Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.

What are polar vectors?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If a vector $2 \hat{i} + 3 \hat{j} + 8 \hat{k}$ is perpendicular to the vector $4 \hat{j} - 4 \hat{i} + α \hat{k}$ , then the value of α is

-1

$\frac{1}{2}$

$- \frac{1}{2}$

1

Pick out the only vector quantities in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction and charge.

Pick out the two scalar quantities in the following list:
force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, reaction as per Newton’s third law, relative velocity.