Home
Class 11
PHYSICS
Given vec(A)=5hat(i)+2hat(j)+4hat(k). Fi...

Given `vec(A)=5hat(i)+2hat(j)+4hat(k)`. Find (a) `|vec(A)|` and (b) the direction cosines of vector `vec(A)`.

Text Solution

AI Generated Solution

To solve the problem, we need to find the magnitude and the direction cosines of the vector \(\vec{A} = 5\hat{i} + 2\hat{j} + 4\hat{k}\). ### Step 1: Calculate the Magnitude of Vector \(\vec{A}\) The magnitude of a vector \(\vec{A} = a\hat{i} + b\hat{j} + c\hat{k}\) is given by the formula: \[ |\vec{A}| = \sqrt{a^2 + b^2 + c^2} ...
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 3.1|19 Videos

  • VECTORS

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 3.2|13 Videos

  • TRAVELLING WAVES

    CENGAGE PHYSICS ENGLISH|Exercise Integer|9 Videos

  • WORK, POWER & ENERGY

    CENGAGE PHYSICS ENGLISH|Exercise Archives (integer)|4 Videos

Similar Questions

Explore conceptually related problems

If vec(A)= 2hat(i)+4hat(j)-5hat(k) then the direction of cosins of the vector vec(A) are

If vec(a) = 2hat(i) + hat(j) - hat(k) and vec(b) = hat(i) - hat(k) , then projection of vec(a) on vec(b) will be :

Given vec(A) = 2hat(i) + 3hat(j) and vec(B) = hat(i) + hat(j) . What is the vector component of vec(A) in the direction of vec(B) ?

The position vectors of points A, B, C and D are : vec(A) = 3hat(i) + 4hat(j) + 5hat(k), vec(B) = 4hat(i) + 5hat(j) + 6hat(k) vec(C ) = 7hat(i) + 9hat(j) + 3hat(k) and vec(D) = 4hat(i) + 6hat(j) Then the displacement vectors vec(AB) and vec(CD) are :

If vec(a) = hat(i) + hat(j) + 2 hat(k) , vec(b) = 2 hat(j) + hat(k) and vec (c) = hat(i) + hat(j) + hat(k) . Find a unit vector perpendicular to the plane containing vec(a), vec(b), vec(c)

IF vec(A) = 5hat(i) + 12hat(j) and vec(B) = 3hat(i) + 4hat(j) , find component of vec(A) in the direction of vec(B) .

If vec(A)=2hat(i)+3hat(j)-hat(k) and vec(B)=-hat(i)+3hat(j)+4hat(k) , then find the projection of vec(A) on vec(B) .

If vec(A)=2hat(i)+hat(j)+hat(k) and vec(B)=hat(i)+hat(j)+hat(k) are two vectors, then the unit vector is

Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

Let vec(a)=hat(i)+4 hat(j)+2hat(k), vec(b)=3 hat(i)-2 hat(j)+7 hat(k) and vec(c)=2hat(i)-hat(j)+4hat(k) . Find a vector vec(p) which is perpendicular to both vec(a) and vec(b) and vec(p). vec(c)=18 .